Question

(Please Answer Quickly) Find the distance between the point and the plane. (Round your answer to three decimal places.)

(4, 2, 1)

x − y + 2z = 6

Answer 1

Answer:

• 0.816

Step-by-step explanation:

The formula used to find the distance between the point and the plane is:

• $D = | ax_0 + by_0 + cz_0 + d| /\sqrt{a^2+b^2+c^2}$, where

ax + by + cz + d = 0 is the plane and (x₀, y₀, z₀) is the point.

It is obvious that:

• a = 1, b = - 1, c = 2 and d = - 6,
• x₀ = 4, y₀ = 2, z₀ = 1.

Substitute and calculate:

• $D = | 1*4 - 1*2 + 2*1 - 6| /\sqrt{1^2+(-1)^2+2^2}=|-2|/\sqrt{6} =2/\sqrt{6}= 0.816$