Question

The intersection of the spheres $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 7 x - 2 y - z = 13$and $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 3 x + 3 y + 4 z = 8$is the same as the intersection of one of the sphere and the plane

• A. $2 x - y - z = 1$
• B. $x - 2 y - z = 1$
• C. $x - y - 2 z = 1$
• D. $x - y - z = 1$

Answer 1

Answer: (A)

$2 x - y - z = 1$

Answer 2

We have the spheres $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 7 x - 2 y - z - 13 = 0$and $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 3 x + 3 y + 4 z - 8 = 0$

Required plane is $S _ { 1 } - S _ { 2 } = 0$

∴ $( 7 x + 3 x ) - ( 2 y + 3 y ) - ( z + 4 z ) - 5 = 0$

i.e. $10 x - 5 y + ( - 5 z ) - 5 = 0$

⇒ $2 x - y - z = 1$ .