Q.

The plane P1:4x+7y+4z+81=0 is rotated through a right angle about its line of  intersection with the plane P2:5x+3y+10z−25=0 . If P3=0 is the equation of  plane P1 in its new position and if k is the distance of P3=0 from origin, then k=

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Detailed Solution

Since Angle between 4x+7y+4z+81=0 and (4+5λ)x+(7+3λ)y+(4+10λ)+81−25λ=0 is π2⇒λ=−1∴p3≡x−4y+6z−106=0 Since the distance from (0,0) to P3 is k∴k=10653=253⇒k=212
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The plane P1:4x+7y+4z+81=0 is rotated through a right angle about its line of  intersection with the plane P2:5x+3y+10z−25=0 . If P3=0 is the equation of  plane P1 in its new position and if k is the distance of P3=0 from origin, then k=