First slide

Planes in 3D

Question

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

Moderate

A

$(- \frac{9}{2}, 9, 9)$
B

$(\frac{9}{2}, 9, 9)$
C

$(9, - \frac{9}{2}, 9)$
D

$(9, \frac{9}{2}, 9)$

Solution

Direction ratios of the line joining points P(1,2,3) and Qe3, 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, 4l).
Thus,
$\begin{array}{l} - 4 (- 1) + 2 (3) + 2 (4) = k \\ o r k = 18 \end{array}$
Hence, equation of plane is 2x - y - z = -9 Then, intercepts are (-9/2),9 and 9.

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