Solveeit Logo
Login

Question

Question: The distance of the point (2, 1, –1) from the plane \(x - 2 y + 4 z = 9\) is...

The distance of the point (2, 1, –1) from the plane x−2y+4z=9x - 2 y + 4 z = 9 is

A

1321\frac { \sqrt { 13 } } { 21 }

B

1321\frac { 13 } { 21 }

C

1321\frac { 13 } { \sqrt { 21 } }

D

1321\sqrt { \frac { 13 } { 21 } }

Answer

1321\frac { 13 } { \sqrt { 21 } }

Explanation

Solution

Distance of the plane from (2, 1, –1)

=∣2−2(1)+4(−1)−91+4+16∣=1321= \left| \frac { 2 - 2 ( 1 ) + 4 ( - 1 ) - 9 } { \sqrt { 1 + 4 + 16 } } \right| = \frac { 13 } { \sqrt { 21 } }