CAIE A-Level Mathematics 3.7.2 Vector operations

CAIE A-Level Mathematics 3.7.2 Vector operations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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

How this is tested

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

Question 11(a)

[Maximum number: 2]
Figure for Question 11(a) — CAIE A-Level Mathematics

Relative to the origin O, the position vectors of the points A, B and C are

OA→=4i−2j,OB→=2i+8j+4k, and OC→=−2i+6k\overrightarrow{O A}=4 \mathbf{i}-2 \mathbf{j}, \overrightarrow{O B}=2 \mathbf{i}+8 \mathbf{j}+4 \mathbf{k} \text {, and } \overrightarrow{O C}=-2 \mathbf{i}+6 \mathbf{k}

The midpoint of AB is M, as shown in the diagram.

Find the vectors MB→\overrightarrow{M B} and MC→\overrightarrow{M C}.