First slide

Planes in 3D

Question

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

Moderate

A

$x - y - z = 1$
B

$x - 2 y - z = 1$
C

$x - y - 2 z = 1$
D

$2 x - y - z = 1$

Solution

The given spheres are
$x^{2} + y^{2} + z^{2} + 7 x - 2 y - z = 13$ --------(i)
and $x^{2} + y^{2} + z^{2} - 3 x + 3 y + 4 z = 8$ ------(ii)
Subtracting (ii) from (i), we get
$\begin{aligned} 10 x - 5 y - 5 z - 5 = 0 \\ or 2 x - y - z = 1 \end{aligned}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App