Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian.
-8x + 6y + 6z = -3 and 10x + 9y + 3z = -8
A) 1.446 rad
B) 0.331 rad
C) 1.521 rad
D) 1.239 rad

Question

Quizplus · Accepted Answer

The angle between two planes can be found using the dot product of their normal vectors. The normal vectors are (8, 6, 6) and (10, 9, 3). The dot product is 8*10 + 6*9 + 6*3 = 159. The magnitudes are √(8²+6²+6²) = √136 and √(10²+9²+3²) = √190. The cosine of the angle is 159 / (√136 * √190), and the angle is arccos(159 / (√136 * √190)) ≈ 0.331 rad.

Use a Calculator to Find the Acute Angle Between the Planes