=v (say) Direction ratios of L2=2,2,1 Line L passing through origin is perpendicular to L1 and L2. Hence, direction ratios of L is parallel to (L1×L2). ⇒(−2,3,−2) Equation of L⇒
x
2
=
y
−3
=
z
2
=λ (say) Solve L and L1, we get (2λ,−3λ,2λ)=(µ+3,2µ−1,2µ+4) Gives, λ=1,µ=−1 So, intersection point P(2,−3,2). Let Q(2v+3,2v+3,v+2) be required point on L2. Now, PQ=√17 (given) Now, PQ=√17 (given) PQ=√(2v+1)2+(2v+6)2+(v)2 =√17 ⇒(2v+1)2+(2v+6)2+v2=17 (squaring on both sides) ⇒9v2+28v+20=0 On solving, we get v=−2 (rejected),