Vectors

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ASFM – Core – Introduction to Vectors

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9A Part 1 Slides (Courtesy of Owen134866)

Textbook Exercise

All Questions except 4b, 6 & 15

Vectors 1 • 3D and Equations of Lines • CP1 Ex9A • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 1-9

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 704a: Find a vector equation textbfr given a point on the line and the direction of the line. (not yet active)
• 704b: Determine whether two lines with given vector equations are parallel. (not yet active)
• 704c: Find a vector equation textbfr given two points on the line.
• 704d: Determine whether a point lies on a line given its vector equation.
• 704e: Determine unknown values in a coordinate given the vector equation of the line. (not yet active)
• 704: Exam Practice: Vector form of a straight line in 2D and 3D

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Solomon C4 Vectors C & Answers
• Mathshelper (Jon Stone)
  • Vector Lines
• MadAsMaths (T. Madas)
  • Vector Algebra Introduction 3D Vectors Q26 (difficulty 4 of 5)
  • Vectors Exam Questions Part A Q6, 43, 46 (difficulty 2–3 of 5)
  • Vectors Practice Part A The Equation of a Line Q1–28

ASFM – Core – Cartesian Form of a Vector Line

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9A Part 2 Slides (Courtesy of Owen134866)

Textbook Exercise

Questions 4b, 6 & 15

Vectors 2 • Cartesian Equations of 3D Lines • CP1 Ex9A • 🎯

Vectors 3 • Line and Circle Problems • CP1 Ex9A • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 10-12

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 705a: Convert the equation of a straight line from vector form to Cartesian/rectangular form.
• 705b: Convert the equation of a straight line from Cartesian/rectangular form to vector form. (not yet active)
• 705: Exam Practice: Cartesian (rectangular) form of an equation of a straight line in 2D and 3D

Other Videos

Vectors : Cartesian Equation of a Line in 3D : ExamSolutions Maths Revision

Exam solutions second example shows what happens when a direction vector contains a ‘0’ term

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

ASFM – Core – Equations of a Plane in 3D

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9B Part 1 Slides (Courtesy of Owen134866)

Vectors 4 • Planes – Parametric and Cartesian • CP1 Ex9B • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Up to 18:45)

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• Dr Frost Slides 13-15

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 707a: Find an equation of a plane passing through 3 points.
• 707b: Determine whether a point lies on a plane with given vector equation. (not yet active)
• 707: Exam Practice: Vector equations of planes in the form textbfr = textbfa + lambdatextbfb + mutextbfc

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

ASFM – Core – Cartesian Form of a Plane

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9B Part 2 Slides (Courtesy of Owen134866)

Vectors 4 • Planes – Parametric and Cartesian • CP1 Ex9B • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (From 18:45)

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• Dr Frost Slides 16-18

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 709a: Determine the Cartesian equation of a plane given its normal vector and a point on the plane.
• 709b: Determine the equation of a plane in the form textbfrcdottextbfn = p given three points on the plane. (not yet active)
• 709c: Determine the equation of a plane in the form textbfrcdottextbfn = p given its equation expressed in the form textbfr = textbfa + lambda textbfb + mu textbfc (not yet active)
• 709d: Convert between Cartesian/rectangular form and textbfrcdottextbfn = p form of a plane. (not yet active)
• 709: Exam Practice: Cartesian equation of a plane and textbfr cdot textbfn = textbfa cdot textbfn form

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

ASFM – Core – Dot Product Rule

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9C Slides (Courtesy of Owen134866)

Vectors 5 • Scalar Dot Product • CP1 Ex9C • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 19-25

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 708a: Calculate the dot product of two vectors.
• 708b: Calculate the angle between two vectors.
• 708c: Determine the angle formed by the position vectors of 3 points. (not yet active)
• 708d: Determine the area of a triangle formed by the position vectors of 3 points. (not yet active)
• 708e: Show that two vectors are perpendicular. (not yet active)
• 708f: Determine the value of a constant given that two vectors are perpendicular.
• 708g: Determine a vector perpendicular to two others (without using the cross product). (not yet active)
• 708h: Use the distributivity of dot products to solve problems. (not yet active)
• 711a: Determine the angle between two lines with given vector equations.
• 711b: Determine the angle between two lines with given Cartesian equations. (not yet active)
• 708: Exam Practice: Dot/scalar product and angles between vectors
• 711: Exam Practice: Angles between a combination of lines and planes

Other Videos

Dot Product Intuition | BetterExplained

Better explained (Full link to web page here)

Enrichment Video

Dot products and duality | Chapter 9, Essence of linear algebra

3Blue1Brown: Dot products and duality

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• PMT Old C4 Questions
• Solomon C4 Vectors D & Answers
• Mathshelper (Jon Stone)
  • Vector Scalar Product
  • Proof Of Scalar Product Equivalence
• MadAsMaths (T. Madas)
  • Vectors Exam Questions Part A Q10, 18, 21, 23, 31, 35, 41, 42, 62, 66, 80, 110, 113, 123, 129, 130, 161, 163–165 (difficulty 2–5 of 5)
  • Vectors Practice Part A Angles & Vectors Q1–10
• Starting Points Maths
  • Properties of Scalar Product · PDF
  • Angle Between Two Vectors · PDF

ASFM – Core – Finding an Angle between Two Lines

ASFM – Core – All Three Forms of a Plane

ASFM – Core – Angle Between a Line and a Plane

ASFM – Core – Angle Between Two Planes

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9D Slides (Courtesy of Owen134866)

Textbook References

• Acute angles between lines: Q1, 9, 10, 11
• r.n=k form of a plane: Q2, 3, 4
• Angle between the plane and a line: Q5, 6, 12
• Angle between two planes: Q7, 8, 13

Vectors 6 • Scalar Product Equation of Plane • CP1 Ex9D • 🎯

Vectors 7 • Angles between Lines, Planes • CP1 Ex9D • 🎯

Vectors 8 • Problems involving Angles • CP1 Ex9D • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 26-33

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 711c: Determine the angle between a line in vector form and a plane in scalar product form. (not yet active)
• 711d: Determine the angle between a line in vector form and a plane in vector form. (not yet active)
• 711e: Determine the angle between two planes in scalar product form. (not yet active)
• 711: Exam Practice: Angles between a combination of lines and planes

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Solomon C4 Vectors D & Answers
• MadAsMaths (T. Madas)
  • Vectors Exam Questions Part B Q10, 23, 29, 48, 56 (difficulty 2–4 of 5)
  • Vectors Practice Part B Geometric Problems (Planes & Lines) Q3–7

ASFM – Core – Intersections of Vector Lines

ASFM – Core – Intersections of Lines and Planes

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9E Slides (Courtesy of Owen134866)

Vectors 9 • Intersection of Lines • CP1 Ex9E • 🎯

Vectors 10 • Intersections of Lines and Planes • CP1 Ex9E • 🎯

Vectors 11 • Intersections of Planes • CP1 Ex9E • 🎯

Vectors 12 • Intersections Problems • CP1 Ex9E • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 34-38

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 706a: Determine the point of intersection of two lines given their vector equations. (not yet active)
• 706b: Show that two lines with given vector equations do not intersect (i.e. are skew lines). (not yet active)
• 706c: Determine the point of intersection of two lines given their Cartesian equations. (not yet active)
• 706d: Show that two lines with given Cartesian equations do not intersect (i.e. are skew lines). (not yet active)
• 710a: Determine the point of intersection between a line in vector form and a plane in scalar product form. (not yet active)
• 710b: Determine the line of intersection between two planes. (not yet active)
• 706: Exam Practice: Point of intersection of two straight lines in 3D
• 710: Exam Practice: Point of intersection of a line and a plane or a plane and plane

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Undergroundmaths 3 lines

Worksheets

• PMT Old C4 Question on Vector Lines
• Solomon C4 Vectors E & Answers
• MadAsMaths (T. Madas)
  • Vectors Exam Questions Part A Q1, 3, 4, 7–9, 13, 14, 16, 17, 24–29, 32, 34, 36, 45, 47, 50–53, 56, 58, 63, 65, 67, 71, 74, 79, 81–83, 85, 86, 91–93, 96, 98, 101, 104, 106, 107, 109, 111, 114, 117, 121, 122, 126, 132–136, 138, 139, 141, 143, 147, 150, 152 (difficulty 2–5 of 5)
  • Vectors Exam Questions Part B Q25, 57, 61 (difficulty 3–4 of 5)
  • Vectors Practice Part A The Equation of a Line Q29–33
  • Vectors Practice Part B Geometric Problems (Planes & Lines) Q1, 2

ASFM – Shortest Distance Between a Point and a Line

ASFM – Core – Shortest Distance Between Two Parallel Lines

ASFM – Core – Shortest Distance Between Two Skewed Lines

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9F Part 1 Slides (Courtesy of Owen134866)

Ex 9F Q 1-4, 7, 9, 11

Vectors 13 • Shortest Distance between Parallel Lines • CP1 Ex9F • 🎯

Vectors 14 • Shortest Distance between Skew Lines • CP1 Ex9F • 🎯

Vectors 15 • Shortest Distance between Point and Line • CP1 Ex9F • 🎯

Vectors 16 • Worded Shortest Distance between Line and Point • CP1 Ex9F • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 39-42

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 712a: Determine unknown values in a coordinate for a point that has a given distance from a line with a given vector equation. (not yet active)
• 712b: Determine the shortest distance between two parallel lines. (not yet active)
• 712c: Determine the shortest distance between two general lines. (not yet active)
• 712d: Determine the shortest distance between a point and a line given in vector form. (not yet active)
• 712e: Determine the shortest distance between a point and a line given in Cartesian/rectangular form. (not yet active)
• 712: Exam Practice: Shortest distance between points or lines, and lines or planes

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

ASFM – Core – Shortest Distance Between a Point and a Plane

ASFM – Core – Shortest Distance Between a Parallel Line and Plane

ASFM – Core – Shortest Distance Between Two Parallel Planes

ASFM – Core – Reflecting a Point in a Line

ASFM – Core – Reflecting a Point in a Plane

ASFM – Core – Reflecting a Line in a Plane

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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9F Part 2 Slides (Courtesy of Owen134866)

Ex 9F Q5, 6, 8, 10, 12

Vectors 17 • Shortest Distance between Plane and Point/Parallel Planes • CP1 Ex9F • 🎯

Vectors 18 • Shortest Distance between Parallel Planes – Parametric Form • CP1 Ex9F • 🎯

Vectors 19 • Reflecting a Point in a Plane • CP1 Ex9F • 🎯

Vectors 20 • Reflecting a Line in a Plane • CP1 Ex9F • 🎯

Vectors 21 • Modelling exam questions • CP1 Ex9 ExamQ • 🎯

Vectors 22 • Reflection exam question • CP1 Ex9 ExamQ • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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• Dr Frost Slides 43-48

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 712f: Determine the shortest distance from a plane to the origin. (not yet active)
• 712g: Determine the shortest distance from a point to a plane. (not yet active)
• 713a: Determine the coordinate of a point reflected in a plane. (not yet active)
• 713b: Determine the vector equation of a line reflected in a plane. (not yet active)
• 712: Exam Practice: Shortest distance between points or lines, and lines or planes
• 713: Exam Practice: Reflection of points in planes (not yet active)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

External whole topic past paper style questions

• WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Jethwa Maths Starter Activities
• Solomon C4 Vectors F & Answers (Context straight lines)
• PMT Questions by topic
  • Edexcel C4 Vectors
  • AQA C4 Vectors
  • OCR C4 Vectors
  • Edexcel FP3 Vectors (Will need to skip those involving Cross Product)
  • OCR FP3 Vectors
  • OCR MEI C4 Coordinate Geometry 1 & MS, Coordinate Geometry 2 & MS
  • OCR MEI C4 Lines & Planes 1 & MS, Lines & Planes 2 & MS, Lines & Planes 3 & MS, Lines & Planes 4 & MS
  • OCR MEI C4 Scalar Product & MS
• Khan Academy
  • section may be worth consulting (videos only)

Worksheets

• Mathshelper (Jon Stone)
  • Planes Sheet
• Physics & Maths Tutor
  • CP1 Ch.9 Vectors: Questions by topic
• MadAsMaths (T. Madas)
  • Vectors Exam Questions Part A Q20, 37–39, 64, 68, 72, 73, 75, 77, 78, 90, 95, 99, 102, 103, 105, 108, 118, 119, 124, 125, 127, 128, 131, 142, 144–146, 151, 153–155, 158–160, 162, 166 (difficulty 3–5 of 5)
  • Vectors Exam Questions Part B Q42, 66 (difficulty 4–5 of 5)
• Interwoven Maths
  • CP1 vectors practice questions✦ (method guide✦)

Activities

• NRICH (student problems)
  • Vectors & Matrices (Further)