The plane denoted by is rotated through a right angle about its line of intersection…

MATHEMATICS · Subjective · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

The plane denoted by P1:4x+7y+4z+81=0P_1 : 4x + 7y + 4z + 81 = 0 is rotated through a right angle about its line of intersection with the plane P2:5x+3y+10z=25P_2 : 5x + 3y + 10z = 25 . If the plane in its new position be denoted by PP , and the distance of this plane from the origin is dd , then the value of [k2]\left[ \frac{k}{2} \right] (where [.][.] represents greatest integer less than or equal to kk ) is .....

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