Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian.
-9x - 7y - 10z = -9 and- 3x + 10y - 10z = -9
A) 1.557 rad
B) 1.308 rad
C) 0.014 rad
D) 1.535 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 $ \vec{n_1} = \langle 9, -7, -10 \rangle $ and to the second plane is $ \vec{n_2} = \langle -3, 10, -10 \rangle $. The angle $ \theta $ between the planes is given by the formula $ \cos(\theta) = \frac{\vec{n_1} \cdot \vec{n_2}}{|\vec{n_1}| |\vec{n_2}|} $. Calculating this gives $ \theta \approx 1.557 $ radians.

Use a Calculator to Find the Acute Angle Between the Planes