First slide

Planes in 3D

Question

$A plane which is perpendicular to two planes 2 x - 2 y + z = 0 and x - y + 2 z = 4 passes through$
$(1, - 2, 1) . The distance of the plane from the point (1,$ $2, 2) is$

Moderate

A

0
B

1
C

$\sqrt{2}$
D

$2 \sqrt{2}$

Solution

$The equation of the plane passing through the point (1, - 2, 1) and perpendicular to the planes 2 x - 2 y + z = 0 and x - y + 2 z = 4$
$is given by |\begin{array}{ccc} x - 1 & y + 2 & z - 1 \\ 2 & - 2 & 1 \\ 1 & - 1 & 2 \end{array}| = 0$
$or x + y + 1 = 0$
Its distance from the point (1, 2,2) is
$|\frac{1 + 2 + 1}{\sqrt{2}}| = 2 \sqrt{2}$

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