Question

# Given that P(3, 2, −4), Q(5, 4, −6) and R(9, 8, −10) are collinear. Find the ratio in which Q divides PR.

Open in App
Solution

## Let Q(5, 4, −6) divides the line segent joining points P(3, 2, −4) and R(9, 8, −10) in the ratio k : 1 internally. ∴ Then coordinates of Q are (9k+3k+1,8k+2k+1,−10k−4k+1) But it is given that coordinates of Q is (5, 4, −6) ∴ 9k+3k+1=5⇒9k+3=5k+5 ⇒ 4k=2 ⇒ k=12 Thus Q divides the line segment joining points P and R in the ratio 12 i.e. 1:2 internally.

Suggest Corrections
0
Explore more