Line L will be parallel to the line of intersection of P1andP2 Let a,band c be the direction ratios of line L ⇒a+2b−c=0and2a−b+c=0 ⇒a:b:c::1:−3:−5 Equation of line L is
x−0
1
=
y−0
−3
=
z−0
−5
Again foot of perpendicular from origin to plane P1 is (−
1
6
,−
1
3
,
1
6
) ∴Equation of projection of line L on plane P1 is
x+
1
6
1
=
y+
2
6
−3
=
z−
1
6
−5
=k Clearly points 0,−
5
6
,−
2
3
and(−
1
6
,−
1
3
,
1
6
) satisfy the line of projection i.e,M. Alternative Solution Direction ratio of plane can be found by (
→
n1
×
→
n2
)×
→
n1
≡(13,−4,5) So,equation of plane is 13x-4y+5z=0 and point (0,−