CAIE A-Level Mathematics A2 3.7.2 Vector Operations Questions

Practise vector notation, operations and geometric relationships within the AS mathematics syllabus.

Exam points

express and manipulate vectors using standard notation
use vector addition, subtraction and scalar multiplication
apply vector operations to collinearity and geometric problems

[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
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
Accept as coordinates.

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CAIE A-Level Mathematics A2 3.7.2 Vector Operations Questions question 1