If the plane 2x+y−5z=0 is rotated about its line of intersection with the plane 3x−y+4z−7=0 by an angle of 2π, then the plane after rotation passes through the point:
Solutions · 1
Official solution
P1:2x+y−52=0, P2:3x−y+4z−7=0
Family of planes P1 and P2
\[P:{P_1} + \lambda {P_2}\]
\[\therefore\] \[P:(2 + 3\lambda )x + (1 - \lambda )y + ( - 5 + 4\lambda )z - 7\lambda = 0\]
\[\because\] \[P \bot {P_1}\]
\[\therefore\] \[4 + 6\lambda + 1 - \lambda + 25 - 20\lambda = 0\]
\[\lambda = 2\]
\[\therefore\] P:8x−y+32−14=0
It passes through the point (1, 0, 2)