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. \[\therefore \] \[\frac{3m+2n}{m+n}=0\] \[\Rightarrow \] \[3m+2n=0\] \[\Rightarrow \] \[3m=2n\] \[\Rightarrow \] \[\frac{m}{n}=-\frac{2}{3}\]You need to login to perform this action.
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