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Eamcet Mathematics
Co - ordinate Geometry 3D Geometry

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Q.

The plane x + y + z = 0 is rotated through right angle about its line of intersection with the plane 2x+ y + 4 = 0 the equation of the plane in its new position is

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Correct choice: A

Explanation:

Equation of a plane passing through the line of intersection of the plane
x + y + z = 0 and 2x + y + 4 = 0 is
(x + y + z) + k(2x + y + 4) = 0 ………………(1)
If d.r. is 1 + 2k, 1 + k , 1
d.r of x + y + z = 0 is 1, 1, 1
Since both are at right angles thus 1(1 + 2k) + (1 + k) + 1 × 1 = 0
Or 3k + 3 = 0 or k = –1
Thus from (1) the required equation is – x + z –4 = 0
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