11 Vector \(\mathbf{a}\) and vector \(2\mathbf{b}\) are drawn on this grid.
(a) Write vector \(\mathbf{a}\) as a column vector. [2]
(b) Write a column vector that is different in direction but has the same length as vector \(\mathbf{a}\). [1]
(c) On the grid below, draw the vector \(\mathbf{a} - \mathbf{b}\). [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
\(\begin{pmatrix} -3 \\ 1 \end{pmatrix}\)
2
B1 for answer \(\begin{pmatrix} -3 \\ k \end{pmatrix}\) or \(\begin{pmatrix} k \\ 1 \end{pmatrix}\)
No fraction line in vector – but penalise 1 mark only in (a) and (b)
Mark scheme (b)
Answer
Marks
Part marks and guidance
Correct response e.g. a vector \(\begin{pmatrix} p \\ q \end{pmatrix}\) where \(p^2 + q^2 = 10\) or FT their (a)
1FT
Allow correct or FT their (a) Must be numeric and column vector
e.g. \(\begin{pmatrix} \pm 3 \\ \pm 1 \end{pmatrix}\) or \(\begin{pmatrix} \pm 1 \\ \pm 3 \end{pmatrix}\) or \(\begin{pmatrix} \sqrt{10} \\ 0 \end{pmatrix}\) etc but not their \(\begin{pmatrix} -3 \\ 1 \end{pmatrix}\) from (a)
Mark scheme (c)
Answer
Marks
Part marks and guidance
Vector \(\mathbf{a} - \mathbf{b}\) correctly drawn with correct direction arrow on the resultant
3
B2 for \(\mathbf{a} - \mathbf{b}\) correctly drawn but with an incorrect or no direction arrow or or B1 for their \(\begin{pmatrix} -3 \\ 1 \end{pmatrix} - \begin{pmatrix} 0 \\ -2 \end{pmatrix}\) or \(\begin{pmatrix} -3 \\ 3 \end{pmatrix}\) or for drawing \(\begin{pmatrix} -3 \\ 1 \end{pmatrix} - \begin{pmatrix} 0 \\ -2 \end{pmatrix}\) oe on grid as two sides of a potential triangle (condone missing/wrong arrows)
If 0 scored, SC1 for vector \(\begin{pmatrix} -3 \\ 5 \end{pmatrix}\) drawn on grid with correct direction arrow
Full marks may be within a triangle with correct direction arrow B2 may be within a triangle with no direction arrow[s]
