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Line with direction ratios $$a, b, c$$ and plane with normal ratios $$a_1, b_1, c_1$$:
$$ \sin \phi = \frac{|a a_1 + b b_1 + c c_1|}{\sqrt{a^2 + b^2 + c^2} \sqrt{a_1^2 + b_1^2 + c_1^2}} $$
where $$\phi$$ is angle between line and plane.
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Line with direction ratios $$a, b, c$$ and plane with normal ratios $$a_1, b_1, c_1$$:
$$ \sin \phi = \frac{|a a_1 + b b_1 + c c_1|}{\sqrt{a^2 + b^2 + c^2} \sqrt{a_1^2 + b_1^2 + c_1^2}} $$
where $$\phi$$ is angle between line and plane.
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