If the points A ≡(1,2,3), B ≡(3,4,7) and C ≡(-3,-2,-5), then the ratio in which point C divides AB, is

Question

If the points A ≡(1,2,3), B ≡(3,4,7) and C ≡(-3,-2,-5), then the ratio in which point C divides AB, is (A) 3: 1 (B) 2: 5 (C) 2: 3 (D) None of these

Tardigrade Admin · Accepted Answer

Let C divide A B in the ratio k: 1 then C(-3,-2,-5) ≡ ((3 k +1/ k +1), (4 k +2/ k +1), (7 k +3/ k +1)) ⇒ (3 k +1/ k +1)=-3, (4 k +2/ k +1)=-2 and (7 k +3/ k +1)=-5 ⇒ k =-(2/3) from all relations Hence, C divides AB extenally in the ratio 2: 3.

Q. If the points $A \equiv (1, 2, 3), B \equiv (3, 4, 7)$ and $C \equiv (- 3, - 2, - 5)$ , then the ratio in which point $C$ divides $A B$ , is

$3 : 1$

$2 : 5$

$2 : 3$

None of these

Q. If the points A≡(1,2,3),B≡(3,4,7) and C≡(−3,−2,−5), then the ratio in which point C divides AB, is

3:1

2:5

2:3

None of these

Let C divide AB in the ratio k : 1 then C(−3,−2,−5)≡ (k+13k+1​,k+14k+2​,k+17k+3​) ⇒k+13k+1​=−3,k+14k+2​=−2 and k+17k+3​=−5 ⇒k=−32​ from all relations Hence, C divides AB extenally in the ratio 2:3.

Q. If the points $A \equiv (1, 2, 3), B \equiv (3, 4, 7)$ and $C \equiv (- 3, - 2, - 5)$ , then the ratio in which point $C$ divides $A B$ , is

$3 : 1$

$2 : 5$

$2 : 3$