a,b,c are non-coplanar vectors and the three points λa−2b+c,2a+λb−2c,4a+7b−8c are collinear. Let P=λa−2b+c ‌Q=2a+λb−2c ‌R=4a+7b−8c PQ‌=(2a+λb−2c)−(λa−2b+c) ‌=(2−λ)a+(λ+2)b+(−3)c PR‌=(4a+7b−8c)−(λa−2b+c) ‌=(4−λ)a+9b−9c ∵P,Q and R collinear. ∴PQ=kPR ⇒(2−λ)a+(λ+2)b+(−3)c =k(4−λ)a+9kb−9kc ∴‌‌2−λ=k(4−λ)⇒λ+2=9k −3=−9k⇒k=‌