Question

If `vecα and vecβ` are position vectors of two points P and Q respectively, then find the position vector of a point R in QP produced such that QR = `3/2` QP.

Answer 1

Given: `vec(OP) = vecα`

`vec(OQ) = vecβ`

`vec(QP) = 3/2 vec(QP)`

⇒ `2vec(QR) = 3vec(QP)`

⇒ `2(vec(OR) - vec(OQ)) = 3(vec(OP) - vec(OQ))`

⇒ `2vec(OR) - 2vec(OQ) = 3vec(OP) - 3vec(OQ)`

⇒ `2vec(OR) - 2vecβ = 3vecα - 3vecβ`

⇒ `2vec(OR) = 3vecα - 3vecβ + 2vecβ`

⇒ `2vec(OR) = 3vecα - vecβ`

⇒ `vec(OR) = (3vecα - vecβ)/2`

Hence, the position vector of a point R is `(3vecα - vecβ)/2`