Find the equation of the sphere described on the joint of points `Aa n dB` having position vectors `2 hat i+6 hat j-7 hat ka n d-2 hat i+4 hat j-3 hat k ,` respectively, as the diameter. Find the center and the radius of the sphere.

Explanation

If point `P` with positive vector `vecr=xhati+yhatj+hatk` is any point on the sphere, then
`" "vec(AP)*vec(BP)=0`
`" "(x-2)(x+2)+(y-6)(y-4)+(z+7)(z+3)=0`
or `" "(x^(2)-4)+(y^(2)-10y+24)+(z^(2)+10z+21)=0`
or `" "x^(2)+y^(2)+z^(2)-10y+10z+41=0`
The centre of this sphere is (0, 5, -5) and its radius is `sqrt(5^(2)+(-5)^(2)-41)=sqrt(9)=3`