Find the ratio in which the join the `A(2,1,5)a n dB(3,4,3)` is divided by the plane `2x+2y-2z=1.` Also, find the coordinates of the point of division.

Options

A. `7:5`
B. `5:7`
C. `5:3`
D. `3:5`

Answer

B

Explanation

Suppose the plane `2x+2y-2z=1` divides the line joining the points `A(2,1,5)` and `B(3,4,3)` at a point C in the ratio `lamda:1`. Then the coordinates of C are
`((3lamda+2)/(lamda+1),(4lamda+1)/(lamda+1),(3lamda+5)/(lamda+1))`…………….i
Since point C lies on the plane `2x+2y-2z=1`
`:.2((3lamda+2)/(lamda+1))+2((4lamda+1)/(lamda+1))-2((3lamda+5)/(lamda+1))=1`
`=8lamda-4=lamda+1implieslamda=5/7`
So the required ratio si `5/4:1` or `5:7`