Find the distance (correct to two decimal places) between the given parallel planes. Select the correct answer.
$6 x + 7 y - 2 z = 12$ and $12 x + 14 y - 4 z = 30$
A) $0.32$
B) $2.32$
C) $4.32$
D) $6.32$
E) $9.32$

Question

Quizplus · Accepted Answer

The distance between the planes is given by the formula:$$d = \frac{|a_1x_0 + b_1y_0 + c_1z_0 - d_1|}{|\sqrt{a_1^2 + b_1^2 + c_1^2}|} $$where $a_1, b_1, c_1, d_1$ are the coefficients of the first plane and $x_0, y_0, z_0$ is any point on the second plane.Let's choose the point $(0, 0, 0)$ on the second plane. Then, we have:$$d = \frac{|6(0) + 7(0) - 2(0) - 12|}{|\sqrt{6^2 + 7^2 + (-2)^2}|} = \frac{12}{\sqrt{85}} \approx 0.32$$

Find the Distance (Correct to Two Decimal Places) Between the Given