If P(3, 2, - 4), Q(5, 4, - 6) and R(9, 8, - 10) are collinear, then R divides PQ in the ratio

Question

If P(3, 2, - 4), Q(5, 4, - 6) and R(9, 8, - 10) are collinear, then R divides PQ in the ratio (A) 3:2 internally (B) 3:2 externally (C) 2:1 internally (D) 2:1 externally

Tardigrade Admin · Accepted Answer

Let R(9, 8 , -10) divides the join of P(3, 2, -4) and Q(5, 4, - 6) in the ratio k: 1. Then, 9=(5k+3/k+1) ⇒ 9k+9=5k+3 ⇒ 4k=-6 ⇒ k = (-3/2) ∴ Required ratio is 3: 2 externally.

Q. If $P (3, 2, - 4)$ , $Q (5, 4, - 6)$ and $R (9, 8, - 10)$ are collinear, then $R$ divides $PQ$ in the ratio

$3 : 2$ internally

$3 : 2$ externally

$2 : 1$ internally

$2 : 1$ externally

Let $R (9, 8, - 10)$ divides the join of $P (3, 2, - 4)$ and $Q (5, 4, - 6)$ in the ratio $k : 1$ .
Then, $9 = \frac{5 k + 3}{k + 1}$
$\Rightarrow 9 k + 9 = 5 k + 3$
$\Rightarrow 4 k = - 6$
$\Rightarrow k = \frac{- 3}{2}$
$∴$ Required ratio is $3 : 2$ externally.

Q. If P(3,2,−4), Q(5,4,−6) and R(9,8,−10) are collinear, then R divides PQ in the ratio

3:2 internally

3:2 externally

2:1 internally

2:1 externally