The intercepts made on the axes by the plane the which bisects the line joining the points `(1,2,3)` and `(-3,4,5)` at right angles are a. `(-9/2,9,9)` b. `(9/2,9,9)` c. `(9,-9/2,9)` d. `(9,9/2,9,)`

Options

A. `(-(9)/(2),9,9)`
B. `((9)/(2),9,9)`
C. `(9,-(9)/(2),9)`
D. `(9,(9)/(2),9)`

Answer

a

Explanation

Direction ratios of the joining points `P(1, 2, 3) and Q(-3, 4, 5)` are -4, 2, 2 which are the direction ratio of the normal to the plane.
Then, equation of plane is `-4x+2y+2z=k`.
Also this plane passes through the midpoint of `PQ(-1, 3, 4)`. Thus,
`" "-4(-1)+ 2(3)+ 2(4)=k`
or `" "k=18`
Hence, equation of plane is `2x-y-z=-9`
Then, intercepts are `(-9//2), 9 and 9`