F.5_AMATHS_Vector

(a)
PQ
=OQ-OP
=(-2-4)i+(5-(-3))j
=-6i+8j
|PQ|
= √(6^2+8^2)
=10
(b)
The unit vector of PQ
(-6/10)i+(8/10)j
PA
=6[(-6/10)i+(8/10)j]
=(-18/5)i+(24/5)j
12
(a)
AB
=OB-OA
=2i+6j
BC
=OC-OB
=(k-3)i+(-2k-14)j
A,B,C collinear
Then
(k-3)i+(-2k-14)j=t[2i+6j] (t constant)
k-3=2t
-2k-14=6t
=>(k-3)/2=(-2k-14)/6
6k-18=-4k-28
10k=-10
k=-1