Q. The intercepts made on the axes by the plane which bisects the line joining the points (1,2, 3) and $( - 3,\ 4,\ 5)$ at right angles are
A) $\left( - \frac{9}{2},9,9 \right)$
B) $\left( \frac{9}{2},9,9 \right)$
C) $\left( 9,\ - \frac{9}{2},9 \right)$
D) $\left( 9,\frac{9}{2},9 \right)$
Explanation
(a)
Direction ratios of the line joining points $P(1,\ 2,\ 3)$ and $Q( - 3,\ 4,\ 5)$ are $- 4,\ 2,\ 2$ which are direction ratios of the normal to the plane
Then, equation of plane is $- 4x + 2y + 2z = k$
Also this plane passes through the midpoint of $PQ( - 1,\ 3,\ 4)$
$\Rightarrow \ - 4( - 1) + 2(3) + 2(4) = k$
$\Rightarrow k = 18$
$\Rightarrow$ Equation of plane is $2x - y - z = - 9$
Then, intercepts are $( - 9/2),9$ and 9
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.