Question

If p & q are position vectors of P & Q respectively & R divides PQ externally by the ratio 3:2, which one is the position vector of R? a. 2p-3q b. 3p-2q Please provide an explanation as well

Answer 1

b. 3p-2q

Explanation:

Let the position vector of P=p

Let the position vector of Q=q

Point R divides segment PQ in ratio 3:2 externally.

`\text{Position Vector of R }=\frac{\text{(Position Vector of P)m }-\text{(Position Vector of Q) n}}{m-n}`

m:n = 3:2

Therefore:

`\text{Position Vector of R }=(3p -2q)/(3-2)\\=3p-2q`