The equation of the plane which is parallel to the plane x-2y+2z=5 and whose distance from the point (1, 2, 3) is 1, is:

Question

The equation of the plane which is parallel to the plane $x - 2 y + 2 z = 5$ and whose distance from the point (1, 2, 3) is 1, is:

Smart Achievers · Accepted Answer

(3)

Ans. $x - 2 y + 2 z = 6$

Explanation:

$Equation of plane parallel to x - 2 y + 2 z = 5 is$

$x - 2 y + 2 z + k = 0$ ...(i)

$Now, according to question,$

$\frac{1 - 4 + 6 + k}{\sqrt{9}} = \pm 1$

$or$ $k + 3 = \pm 3$

$\Rightarrow$ $k = 0 or - 6$

$∴$ $x - 2 y + 2 z - 6 = 0$

$or$ $x - 2 y + 2 z = 6$

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