Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian.
-4x - 4y + 9z = -10 and -5x - 3y + 7z = 10
A) 0.967 rad
B) 1.478 rad
C) 0.604 rad
D) 0.196 rad

Question

Quizplus · Accepted Answer

The angle between two planes can be found using the dot product of their normal vectors. The normal vector to the first plane is $ \mathbf{n}_1 = \langle 4, -4, 9 \rangle $ and to the second plane is $ \mathbf{n}_2 = \langle -5, -3, 7 \rangle $. The angle $ \theta $ between the planes is given by the formula $ \cos \theta = \frac{\mathbf{n}_1 \cdot \mathbf{n}_2}{\|\mathbf{n}_1\| \|\mathbf{n}_2\|} $. Plugging in the values and solving for $ \theta $ gives $ \theta \approx 0.967 $ radians.

Use a Calculator to Find the Acute Angle Between the Planes