The correct option is C (0,−56,−23)
Line L will lie on one of the angle bisector planes and will be parallel to line of intersection of the given planes.
Also locus of foot of perpendicular of line L in plane P1 will be line M, which will be parallel L.
Foot of perpendicular from (0,0,0) on plane P1 is
Line L will lie on one of the angle bisector planes and will be parallel to line of intersection of the given planes.
Also locus of foot of perpendicular of line L in plane P1 will be line M, which will be parallel L.
Foot of perpendicular from (0, 0, 0) on plane P1 is (16,13,16)
Hence equation of line M
x+161=y+133=z165
where ^i−3^j−5^k is vector parallel to line of intersection of P1 and P2.
On checking (0,56,23), (16,13,16) satisfy the above equation.