Question

find the maximum n minimum distances of the point (1,2,3)from the sphere x^2+y^2+z^2=56​

Answer 1

Answer:

1,2,−1) 

x2+y2+z2=24

length = 12+22+(−1)2=1+4+1=6

Now, F(x,y,z,λ)=(x−1)2+(y−2)2+(z+1)2−λ(x2+y2+z2−24)

⇒x2+1−2x+y2+4−4y+z2+1+2z−λx2−λy2−24λ

=(1+λ)x2+(1−λ)y2−2x+1−4y+4+2z+1+(1−λ)z2+24λ

⇒∂x∂F=2x