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: C

Solution :

Key Idea The coordinate of \[x\] in \[yz-\]plane is 0. Let the point \[R\] divides the line joining the points \[P(2,\,\,4,\,\,5)\] and \[Q(3,\,\,5,\,\,-4)\] in the ratio\[m:n\]. \[\therefore \]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. \[\therefore \]  \[\frac{3m+2n}{m+n}=0\] \[\Rightarrow \]               \[3m+2n=0\] \[\Rightarrow \]               \[3m=2n\] \[\Rightarrow \]               \[\frac{m}{n}=-\frac{2}{3}\]