Find, correct to the nearest degree, the angle between the planes. Select the correct answer.
$$x + y - z = 1,3 x - 13 y + 6 z = 5$$
A) $129 ^ { \circ }$
B) $8 ^ { \circ }$
C) $5 ^ { \circ }$
D) $102 ^ { \circ }$
E) none of these

Question

Quizplus · Accepted Answer

The angle between two planes is given by the angle between their normal vectors. The normal vectors are $\langle 1, 1, -1 \rangle$ and $\langle 3, -13, 6 \rangle$. The dot product of these vectors is $-16$, and their magnitudes are $\sqrt{3}$ and $\sqrt{214}$, respectively. The cosine of the angle is $-16 / (\sqrt{3} \times \sqrt{214})$, which gives an angle of approximately $129^\circ$.

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