Chapter 12 - Vectors and the Geometry of Space - Review - Concept Check - Page 881: 12

Use the normal vectors of the plane. So 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. So 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.

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