If denote the position vectors of points A and B respectively and C is a point on AB such that 3AC = 2AB, then write the position vector of C.

Question

Philoid · Accepted Answer

Given that the position vector points A, B are .

Let us assume that C lies between A and B.

Then AB=AC+BC

Given that 3AC=2AB=2(AC+BC)

⇒ AC=2BC

Therefore AC: BC=1:2

Also, since the ratio is positive, our assumption was correct.

Using section formula,