The coordinates of the point P on the line r→=(i^+j^+k^)+λ(−i^+j^−k^) which .n is nearest to the origin is

Let the point P be (x, y, z),  then the vector xi^+yj^+zk^ will lie on the line. Thus, (x−1)i^+(y−1)j^+(z−1)k^=−λi^+λj^−λk^⇒ x=1−λ,y=1+λ and z=1−λNow point P is nearest to the origin⇒ D=(1−λ)2+(1+λ)2+(1−λ)2 or  dDdλ=−4(1−λ)+2(1+λ)=0⇒λ=13Hence, the point  23,43,23