AS June 2021 Paper 1 Q5
5 Show that the vectors \(\begin{bmatrix}1 \\ -3 \\ 5\end{bmatrix}\) and \(\begin{bmatrix}7 \\ 4 \\ 1\end{bmatrix}\) are perpendicular. [2 marks]
| Scheme | Marks | AO |
|---|---|---|
| Calculates the scalar product of the two vectors. Accept one miscopy of an element, or one incorrect product if the elements are not shown. | M1 | 1.1a |
| Completes a fully correct proof to reach the required result. Must include at least one calculation line and =0 linked with perpendicular conclusion. Ignore incorrect vector magnitudes. | R1 | 2.1 |
| (2 marks) |
Typical solution
\[\begin{aligned}\begin{bmatrix}1 \\ -3 \\ 5\end{bmatrix}\cdot\begin{bmatrix}7 \\ 4 \\ 1\end{bmatrix} &= 1 \times 7 + (-3) \times 4 + 5 \times 1 \\ &= 7 - 12 + 5 = 0\end{aligned}\]\(\therefore\) the two vectors are perpendicular