Not sure about this:

Question

498. Draw an acute-angled triangle ABC, and mark points P and Q on sides AB and AC, respectively, so that AB = 3AP and AC = 3AQ. Express PQ and BC in terms of v = AP and w = AQ.

Answer 1

Vectors and Geometry?

Answer 2

1st step draw a diagram

any acute triangle will do, maybe put A on top B to the left, C to the right

also v = AP w=AQ and AB =3AP & AC = 3AQ

then ...

one method might be use the law of cosines

PQ = square root of (v^2 +w^2 -2vwCosA)

BC = square root of (9v^2 +9w^2 -18vwCosA)