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CGP EDU Academic Team
Published on: August 14, 2026
The plane 4x + 7y + 4z + 81 = 0 is rotated through a right angle about its line of intersection with the plane 5x + 3y + 10z = 25. If the equation of the plane in its new position is x - 4y + 6z = K, then the value of K is
Text Solution
Verified by ExpertsThe correct answer is:
A
106
The equation of the plane through the line of intersection of the planes is
(4x + 7y + 4z + 81) + 
(5x + 3y + 10z - 25) = 0
(4 + 5 
)x + (7 + 3 
)y + (4 + 10 
)z + (81 - 25 
) = 0
Which is parallel to x - 4y + 6z = K
So, -16 - 20A = 7 + 3A
23 
= -23
=1
and 
Hence, K = 106
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