Question

The distance between the line $\frac{x - 1}{3} = \frac{y + 2}{- 2} = \frac{z - 1}{2}$ and the plane $2x + 2y - z = 6$ is

• A. 9
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (D)

3

Answer 2

Obviously the line and the plane are parallel, so to find the distance between the line and the plane, take any point on the line i.e., (1, – 2, 1). Now the perpendicular distance of the point (1, – 2, 1) from the plane will be the required distance.

Hence distance $= \left| \frac { 2 ( 1 ) + 2 ( - 2 ) - 1 ( 1 ) - 6 } { \sqrt { 2 ^ { 2 } + 2 ^ { 2 } + 1 ^ { 2 } } } \right| = \frac { 9 } { \sqrt { 9 } } = 3$ .