question_answer

The ratio in which the line joining (2, 4, 5), (3, 5,-  4) is divided by the yz plane, is

A) 2 : 3

B) 3 : 2

C) -2 : 3

D) 4 : - 3

Correct Answer: A

Solution :

[a] Let the point R divides the line joining the points P(2, 4, 5) and Q(3, 5, -4) in the ration m:n. \[\therefore \]      The coordinate of R is \[\left( \frac{3m-2n}{m+n},\frac{5m-4n}{m+n},\frac{-4m+5n}{m+n} \right)\] Since, the point R is on yz-plane, therefore x-coordinate will be zero. \[\therefore \frac{3m-2n}{m+n}=0\Rightarrow 3m-2n=0\Rightarrow 3m=2n\]\[\Rightarrow \frac{m}{n}=\frac{2}{3}\]