angle between planes

Question

Two planes are perpendicular if

RankGuru · Accepted Answer

1. **Theory**: The angle between two planes is equal to the angle between their normals.
2. **Normal Vectors**: For planes $A_1x + B_1y + C_1z + D_1 = 0$ and $A_2x + B_2y + C_2z + D_2 = 0$, the normal vectors are $\vec{n_1} = (A_1, B_1, C_1)$ and $\vec{n_2} = (A_2, B_2, C_2)$.
3. **Perpendicularity Condition**: Vector $\vec{n_1} \perp \vec{n_2} \iff \vec{n_1} \cdot \vec{n_2} = 0$.
4. **Expansion**: $A_1A_2 + B_1B_2 + C_1C_2 = 0$.

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angle between planes

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