A point on XOZ- plane divides tha join of (5,-3,-2) and (1,2,-2) at

Options

A. `((13)/(5),0,-2)`
B. `((13)/(5),0,2)`
C. `(5,0,2)`
D. `(5,0,-2)`

Answer

A

Explanation

Let point `P(x,y,z)` divides the line joining the points A and B in the ratio `m:1 ` .

since , point P is on XOZ-plane ` :.` y coordinate =0
`implies (2m-3)/(m+1)=0`
`implies m=(3)/(2)`
Now , ` x=(3+ 2 xx 5)/(3+2)=(13)/(5)`
and ` z=( 3 xx (-2)+2 xx (-2))/(5)=-2 `
`:.` Required point is `((13)/(5),0,-2)` .