Find, correct to the nearest degree, the angle between the planes. $x + y - z = 1,5 x - 13 y + 10 z = 5$
A) $127 ^ { \circ }$
B) $12 ^ { \circ }$
C) $123 ^ { \circ }$
D) $7 ^ { \circ }$
E) none of these

Question

Quizplus · Accepted Answer

The angle between two planes can be found using the dot product of their normal vectors. The normal vectors are $ \langle 1, 1, -1 \rangle $ and $ \langle 5, -13, 10 \rangle $. The dot product is $-8$, and the magnitudes are $\sqrt{3}$ and $\sqrt{294}$. The cosine of the angle is $-8 / (\sqrt{3} \times \sqrt{294})$, which gives an angle of approximately $127^\circ$.

Find, Correct to the Nearest Degree, the Angle Between the Planes