Even More Vectors

Previous Section: Core Pure 1 & 2 General Support

Next Section: Conic Sections Part 1

Word Doc

PDF

Tutorial Videos

Vector Product or Cross Product (part 1) : ExamSolutions Maths Revision

Vector Product or Cross Product (part 1) : ExamSolutions Maths Revision by ExamSolutions

A-Level Further Maths F6-02 Vector Product: Calculating the Vector Product

A-Level Further Maths F6-02 Vector Product: Calculating the Vector Product by TLMaths

A Level Further Maths | Further Pure 1 | Vector Product 🧮

A Level Further Maths | Further Pure 1 | Vector Product by AJMaths

Download Blank Notes

Download Slides

No Live Lesson from Bicen Maths Yet

Download Blank Notes

(Courtesy of Bicen Maths)

Download Slides

• Dr Frost Slides 1-14

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

• 750a: State the vector product of a combination of textbfi, textbfj and textbfk (not yet active)
• 750b: Use the vector product to find a vector perpendicular to two others. (not yet active)
• 750c: Recognise properties of vector products, including the effect of reversing the order in the product and the vector product of the same vector. (not yet active)
• 750d: Determine the vector product of two vectors based on the position vectors of three points. (not yet active)
• 750: Exam Practice: Vector product textbfa × textbfb of two vectors

Enrichment Video

Cross products | Chapter 10, Essence of linear algebra

3Blue1Brown: Cross products

Alternative Handouts

Online Platform

Tutorial Videos

Vector Product applications – Area of a Triangle : ExamSolutions Maths Revision

Vector Product applications – Area of a Triangle : ExamSolutions Maths Revision by ExamSolutions

Vector Product applications – Area of a Parallelogram : ExamSolutions Maths Revision

Vector Product applications – Area of a Parallelogram : ExamSolutions Maths Revision by ExamSolutions

A-Level Further Maths F6-12 Vector Product: Find the Area of the triangle OAB

A-Level Further Maths F6-12 Vector Product: Find the Area of the triangle OAB by TLMaths

1.2 Finding Areas (FP1 – Chapter 1: Vectors)

1.2 Finding Areas (FP1 – Chapter 1: Vectors) by Hinds Maths

Download Blank Notes

Download Slides

No Live Lesson from Bicen Maths Yet

Download Blank Notes

(Courtesy of Bicen Maths)

Download Slides

• Dr Frost Slides 15-21

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

• 750e: Determine the area of a triangle using the vector product of vectors forming two sides of the triangle. (not yet active)
• 750f: Determine the area of a triangle given the position vector of the vertices, using the vector product. (not yet active)
• 750g: Determine the area of a parallelogram using a vector product. (not yet active)
• 750: Exam Practice: Vector product textbfa × textbfb of two vectors

Alternative Handouts

Online Platform

Tutorial Videos

Vectors – Triple Scalar Product : ExamSolutions Maths Revision

Vectors – Triple Scalar Product : ExamSolutions Maths Revision by ExamSolutions

Volume of a Parallelepiped : ExamSolutions Maths Revision

Volume of a Parallelepiped : ExamSolutions Maths Revision by ExamSolutions

Volume of a tetrahedron using the triple scalar product : ExamSolutions Maths Revision

Volume of a tetrahedron using the triple scalar product : ExamSolutions Maths Revision by ExamSolutions

1.3 Scalar Triple Product (FP1 – Chapter 1: Vectors)

1.3 Scalar Triple Product (FP1 – Chapter 1: Vectors) by Hinds Maths

Download Blank Notes

Download Slides

No Live Lesson from Bicen Maths Yet

Download Blank Notes

(Courtesy of Bicen Maths)

Download Slides

• Dr Frost Slides 22-28

Extra Questions

• Dr Frost Questions (very short)

Key Skills

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

• 752a: Calculate a scalar triple product. (not yet active)
• 752b: Calculate the volume of a parallelepiped using a scalar triple product given vectors for three of its edges. (not yet active)
• 752c: Calculate the volume of a parallelepiped using a scalar triple product given position vectors for some its vertices. (not yet active)
• 752d: Determine an unknown value in a coordinate of a parallelepiped given its volume. (not yet active)
• 752e: Calculate the volume of a tetrahedron using a scalar triple product given vectors for three of its edges. (not yet active)
• 752f: Calculate the volume of a tetrahedron using a scalar triple product given the position vectors of its vertices. (not yet active)
• 752g: Determine the volume of a truncated tetrahedron. (not yet active)
• 752: Exam Practice: Scalar triple product textbfa cdot textbfb × textbfc

Alternative Handouts

Online Platform

Tutorial Videos

A-Level Further Maths F6-14 Vector Product: The Vector Product Form of a Line

A-Level Further Maths F6-14 Vector Product: The Vector Product Form of a Line by TLMaths

1.4 Straight Lines (FP1 – Chapter 1: Vectors)

1.4 Straight Lines (FP1 – Chapter 1: Vectors) by Hinds Maths

Direction Cosines of a Vector | Mr Mathematics

Direction Cosines of a Vector | Mr Mathematics by Mr Mathematics | Jonathan Robinson

A Level Further Maths | Further Pure 1 | Straight Lines 🧮

A Level Further Maths | Further Pure 1 | Straight Lines by AJMaths

Download Blank Notes

Download Slides

No Live Lesson from Bicen Maths Yet

Download Blank Notes

(Courtesy of Bicen Maths)

Download Slides

• Dr Frost Slides 29-34

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

• 753a: Determine the equation of a straight line in the form (textbfr-textbfa)× textbfb = 0 using two points on the line. (not yet active)
• 753b: Determine the equation of a straight line in the form (textbfr × textbfa = textbfb using two points on the line. (not yet active)
• 753c: Determine the direction cosines of the lines l, m and n (not yet active)
• 753d: Determine the coordinates of a point on a line with given vector product equation and one of the cosines. (not yet active)
• 753e: Determine the Cartesian equation of a line by calculating the direction cosines. (not yet active)
• 753: Exam Practice: Equations of lines and planes and shortest distances using vector products

Alternative Handouts

Online Platform

Worksheet & Activities

Tutorial Videos

Vectors – Shortest Distance between Skew Lines : ExamSolutions Maths Revision

Vectors – Shortest Distance between Skew Lines : ExamSolutions Maths Revision by ExamSolutions

1.5 Solving Geometrical Problems (FP1 – Chapter 1: Vectors)

1.5 Solving Geometrical Problems (FP1 – Chapter 1: Vectors) by Hinds Maths

A Level Further Maths | Further Pure 1 | Solving Geometrical Problems 🧮

A Level Further Maths | Further Pure 1 | Solving Geometrical Problems by AJMaths

Intersection Line of 2 Planes – How to Find It – Step by Step Method & Explanation – Vector Equation

Intersection Line of 2 Planes – How to Find It – Step by Step Method & Explanation – Vector Equation by Radford Mathematics

Download Blank Notes

Download Slides

No Live Lesson from Bicen Maths Yet

Download Blank Notes

(Courtesy of Bicen Maths)

Download Slides

• Dr Frost Slides 35-46

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

• 753f: Determine the Cartesian equation of a plane given vector equations of a line and a point on the plane. (not yet active)
• 753g: Determine the normal vector to a plane given its equation in the form textbfr = textbfa + lambdatextbfb + gammatextbfc (not yet active)
• 753h: Determine the equation of a plane in the form textbfrcdottextbfn = p given three points that lie on the plane. (not yet active)
• 753i: Determine the Cartesian equation of a plane given three points that lie on the plane. (not yet active)
• 753j: Determine the vector equation of the line of intersection of two planes with equations in the form textbfr cdot textbfn = p (not yet active)
• 753k: Determine the vector product equation textbfr × textbfa = textbfb of the line of intersection of two planes with equations in the form textbfr cdot textbfn = p or textb (not yet active)
• 753l: Determine the shortest distance between two skew lines with given vector equations, using the vector product. (not yet active)
• 753m: Determine the vector equation of a line formed from the matrix transformation of another line. (not yet active)
• 753: Exam Practice: Equations of lines and planes and shortest distances using vector products

Alternative Handouts

Activities

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.)
• WW Dr Frost Style Summary Sheet Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)

Worksheets

• Physics & Maths Tutor
  • FP1 Ch.1 Vectors: Questions by topic
• MadAsMaths (T. Madas)
  • Vectors Exam Questions Part B Q14, 16, 46, 60, 62, 65, 68 (difficulty 3–5 of 5)