First slide

Planes in 3D

Question

The equation of the plane which is at a distance $3 \sqrt{3}$ units from origin and the normal to which is equally inclined to coordinate axes is

Moderate

A

$x + y + z = 9$
B

$x + y - z = 9$
C

$x + y + z = 3$
D

$x + y + z = 0$

Solution

Dc's of normal $(l, m, n) = (\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}})$
$P = \sqrt{3}$
Equation of plane $l x + m y + n z = P$

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