The equation of the plane through (1, 2, 3) and parallel to the plane 2 x + 3 y - 4 z = 0 is:

Question

The equation of the plane through (1, 2, 3) and parallel to the plane $2 x + 3 y - 4 z = 0$ is:

Smart Achievers · Accepted Answer

(4)

Ans. $2 x + 3 y - 4 z + 4 = 0$

Explanation:

Plane parallel to the plane $2 x + 3 y - 4 z = 0$ is

$2 x + 3 y - 4 z + k = 0$ ...(i)

Also plane (i) is passing through (1, 2, 3).

$∴$ $(2) (1) + (3) (2) - (4) (3) + k = 0$

$\Rightarrow$ $k = 4$

$∴$ Required plane is $2 x + 3 y - 4 z + 4 = 0 .$

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