CAIE A-Level Mathematics 3.7.2 Vector operations

Practise adding, subtracting and scaling vectors to model shapes, reflections and position vectors in 3D geometry.

Exam points

use vector addition and subtraction to find missing vertices in parallelograms or trapezia

[Maximum number: 2]

With respect to the origin O, the position vectors of the points A and B are given by $\overrightarrow{O A}=\left(\begin{array}{r}1 \\ 2 \\ -1\end{array}\right)$ and $\overrightarrow{O B}=\left(\begin{array}{l}0 \\ 3 \\ 1\end{array}\right)$ .

The point C lies on l and is such that $\overrightarrow{A C}=3 \overrightarrow{A B}$ .

Find the position vector of C.

Use a correct method to find the position vector of C
M1
e.g. $\mathbf{O C}=\mathbf{O A}+\mathbf{A C}=\left(\begin{array}{c}1-3 2+3 -1+6\end{array}\right)$
Obtain answer -2 i+5 j+5 k, or equivalent
A1
Accept as coordinates.

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3.7.2—Vector operations question 1