1.17: Past-paper question 8

4PM1/2/June/2025 — Question 8 · 11 marks

1.17 diagram 1
Figure 2 shows triangle OAB\displaystyle OAB with
OA→=3u+vOB→=−u+2v\overrightarrow{OA} = 3\mathbf{u} + \mathbf{v} \quad \overrightarrow{OB} = -\mathbf{u} + 2\mathbf{v}
(a) Find AB→\displaystyle \overrightarrow{AB} as a simplified expression in terms of u\displaystyle \mathbf{u} and v\displaystyle \mathbf{v}
(2)
Point C\displaystyle C is such that AC\displaystyle AC is parallel to OB\displaystyle OB
Given that OC→=μv\displaystyle \overrightarrow{OC} = \mu\mathbf{v}
(b) find the value of μ\displaystyle \mu
(4)
The lines OC\displaystyle OC and AB\displaystyle AB intersect at point X\displaystyle X
Point D\displaystyle D lies on OC→\displaystyle \overrightarrow{OC} such that
area of triangle BOX\displaystyle BOX : area of triangle BXD=2:3\displaystyle BXD = 2 : 3
Using a vector method,
(c) find BD→\displaystyle \overrightarrow{BD} as a simplified expression in terms of u\displaystyle \mathbf{u} and v\displaystyle \mathbf{v}
(5)