Question

If the position vectors of the point A, B and C are -2i + j -k, -4i + 2i + 2k and 6i - 3j - 13k respectively and AB = λAC, then find the value of λ.

Answer 1

position vector of A = -2i + j - k
position vector of B = -4i + 2j + 2k
position vector of C = 6i - 3j - 13k

now, AB = position vector of B - position vector of A
= (-4i + 2j + 2k ) - ( -2i + j - k )
= -2i + j + 3k

similarly, AC = position vector of C - position vector of A
= (6i - 3j - 13k ) - (-2i + j - k)
= 8i - 4j - 12k

A/C to question, AB = λAC
-2i + j + 3k = λ(8i - 4j - 12k)
λ = -1/4