3. \(\mathbf{p} = \begin{pmatrix}5\\4\end{pmatrix}\) and \(\mathbf{q} = \begin{pmatrix}1\\-1{\cdot}5\end{pmatrix}\)
(a) Work out the column vector \(2\mathbf{p} - \mathbf{q}\). [2]
(b) The grid shows the vector \(\mathbf{q}\).On the same grid, draw the vector \(-3\mathbf{q}\). [2]
Mark scheme (a)
Scheme
Marks
Comments
\(\begin{pmatrix}9\\9.5\end{pmatrix}\)
B2
B1 for each element or for \(2\mathbf{p} = \begin{pmatrix}10\\8\end{pmatrix}\) or equivalent seen or for \(\left(\dfrac{9}{9.5}\right)\) or for \(\begin{matrix}9\\9.5\end{matrix}\) or for \(\dfrac{9}{9.5}\)
Mark scheme (b)
Scheme
Marks
Comments
Line of correct length and direction:
B2
B1 for correct length but direction omitted or incorrect or for correct direction but incorrect length
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