First slide

Planes in 3D

Question

$Equation of the plane such that foot of altitude drawn from (- 1, 1, 1) to the plane has the$ $coordinate (3, - 2, - 1) is$

Moderate

A

$x + y + z = 0$
B

$4 x - 3 y - 2 z = 20$
C

$3 x + y - z = 8$
D

$4 x + 3 y - z = 7$

Solution

$Clearly, the direction ratios of normal to the plane are 4, - 3, - 2 .$
$Thus equation of plane will be 4 x - 3 y - 2 z = d .$
$It will necessarily pass though (3, - 2, - 1)$
$ie., d = 12 + 6 + 2 = 20$
$\begin{array}{l} Thus the equation of plane is \\ 4 x - 3 y - 2 z = 20 \end{array}$

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