Find, correct to the nearest degree, the angle between the planes. Select the correct answer.
$$x + y - z = 1,11 x - 9 y + 22 z = 5$$
A) $116 ^ { \circ }$
B) $24 ^ { \circ }$
C) $13 ^ { \circ }$
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 (1, 1, -1) and (11, -9, 22). The dot product of these vectors is 1*11 + 1*(-9) + (-1)*22 = -20. The magnitudes are √3 and √686. The cosine of the angle is -20/(√3 * √686), which gives an angle of approximately 116 degrees.

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