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10 cards from this deck
Find angles; plane equations; line/plane/plane angles
a⋅b=∣a∣∣b∣cosθ\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}| |\mathbf{b}| \cos \thetaa⋅b=∣a∣∣b∣cosθ
Direction vectors
cosθ=b1⋅b2∣b1∣∣b2∣\cos \theta = \frac{\mathbf{b}_1 \cdot \mathbf{b}_2}{|\mathbf{b}_1||\mathbf{b}_2|}cosθ=∣b1∣∣b2∣b1⋅b2
r⋅n=k\mathbf{r} \cdot \mathbf{n} = kr⋅n=k
Vector perpendicular to the plane
Normal vectors
cosθ=n1⋅n2∣n1∣∣n2∣\cos \theta = \frac{\mathbf{n}_1 \cdot \mathbf{n}_2}{|\mathbf{n}_1||\mathbf{n}_2|}cosθ=∣n1∣∣n2∣n1⋅n2
Complementary angles
sinθ=b⋅n∣b∣∣n∣\sin \theta = \frac{\mathbf{b} \cdot \mathbf{n}}{|\mathbf{b}||\mathbf{n}|}sinθ=∣b∣∣n∣b⋅n
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