Position vectors with ratio

2. The points A and B have position vectors 3i − 2j + k and −i + 2j − 7k.
Find position vector of the point P on AB such that
AP : P B = 3 : 1

What have you done so far? Do you have a method for this?

ive worked out what AB is

Good. So, what fraction of the way along AB is P going to be?

3/4

Yep. So AP = (3/4) AB

Then the position vector of P, that is OP, is simply OA + AP.

so we do the opposite and add

so we do the opposite and add

final answer i got is j-5k or 0i+j-5k

Agreed.

thanks.

there is another question that i need help with.

Given three nonzero vectors a, b and c, are the following statements True or False? Give a short reason or counter-example to justify your answer.
(a) If a ⊥ b and also b ⊥ c then a ⊥ c.
(b) If a ⊥ b and also a ⊥ c then a ⊥ (b + c).
(c) If a ⊥ b and also b ⊥ c then b ⊥ (a − c).
(d) If a ⊥ (b + c) and also a ⊥ (b − c) then a ⊥ b.