CAIE A-Level Mathematics 3.7.3 Position vectors

CAIE A-Level Mathematics 3.7.3 Position vectors
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise finding position vectors, displacement vectors, magnitudes and unit vectors from 2D or 3D coordinate information.

How this is tested

  • calculate vector magnitudes to compare lengths or prove triangles are isosceles
  • form position vectors for points on a line, then solve modulus conditions for the parameter
  • find unit vectors by dividing a direction vector by its magnitude

Question 10(a)

[Maximum number: 3]

With respect to the origin O, the points A, B and C have position vectors given by

OA→=2i−j−6k,OB→=bi−2j+3k and OC→=−4i+5j−2k.\overrightarrow{O A}=2 \mathbf{i}-\mathbf{j}-6 \mathbf{k}, \quad \overrightarrow{O B}=b \mathbf{i}-2 \mathbf{j}+3 \mathbf{k} \quad \text { and } \quad \overrightarrow{O C}=-4 \mathbf{i}+5 \mathbf{j}-2 \mathbf{k} .

It is given that ∣AB→∣=∣BC→∣|\overrightarrow{A B}|=|\overrightarrow{B C}|.

Find the value of b.