Find the ratio in which the line joining the points `(1,2,3)a n d(-3,4,-5)` is divided by the `x y-p l a n e` . Also, find the coordinates of the point of division.

Options

A. 3:5 internally
B. 5:3 externally
C. 3:5 externally
D. 5:3 internally

Answer

A

Explanation

Suppose the line joining the points `P(1,2,3)` and `Q(-3,4,-5)` is divided by the xy-plane at a point `R` in the ratio `lamda:1`. Then the coordinates of `R` are
`((-3lamda+1)/(lamda+1),(4lamda+2)/(lamda+1),(-5lamda+3)/(lamda+1))`…………..i
Since `R` lies on xy plane i.e. `z=0`
`:.(-5 lamda+3)/(lamda+1)=0implieslamda=3/5`
So, the required ratio is `3/5:1` or `3:5` internally.