Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 12 - Review - Concept Check - Page 883: 12

Answer

Use the normal vectors of the plane. Say planes $p_1$ and $p_2$ have normal vectors $n_1$ and $n_2$ respectively. Now find the norm of the normal vectors and find their dot product and use the formula$$ |n_1n_2|=|n_1||n_2|cos\theta$$$$\implies cos\theta=\frac{|n_1n_2|}{|n_1||n_2|}$$ and solve the angle. If the angle $\theta$ is acute or right, then it is the angle between the two planes. If the angle $\theta$ is obtuse, then subtract it from $180^\circ$; then it will be the angle between the two planes.

Work Step by Step

Use the normal vectors of the plane. Say planes $p_1$ and $p_2$ have normal vectors $n_1$ and $n_2$ respectively. Now find the norm of the normal vectors and find their dot product and use the formula$$ |n_1n_2|=|n_1||n_2|cos\theta$$$$\implies cos\theta=\frac{|n_1n_2|}{|n_1||n_2|}$$ and solve the angle. If the angle $\theta$ is acute or right, then it is the angle between the two planes. If the angle $\theta$ is obtuse, then subtract it from $180^\circ$; then it will be the angle between the two planes.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.