Find the value \(k\) so that \(k(\mathbf{a} - \mathbf{b}) = \mathbf{c}\). [2]
Mark scheme (a)
Answer
Marks
Part marks and guidance
(i) Draws vector \(\begin{pmatrix} 4 \\ 2 \end{pmatrix}\)
(ii) and Draws vector \(\begin{pmatrix} 0 \\ 2 \end{pmatrix}\)
2
B1 for each
In (a), penalise first instance only where direction arrow is omitted Condone good freehand mark intention
Could be part of correct vector triangle
Mark scheme (b)
Answer
Marks
Part marks and guidance
They are different in direction oe
1
Accept correct comments that mention the directions of the vectors
Accept any comment implying the directions of the 2 vectors are different e.g. ‘They are not parallel’ ‘They are going in different directions’ ‘They are going in opposite \(x\)–directions’ ‘Vector A is a [vertical] reflection of vector B’ ‘One goes left, the other goes right’ ‘One goes in positive direction the other goes in negative direction’ ‘One has –2 and the other has 2’ Condone ‘They are going in opposite directions’
Do not accept mention of just 1 vector only unless the reason clearly implies a comparison e.g. Do not accept ‘Vector a goes right’ ‘One of them has a minus sign’
