Porisma
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Vectors: planes, normals and distances

Meet a line and a plane · Diagrams

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Acute and obtuse angles to the normal

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Two schematic source cases share a plane, its normal n, the line and a dashed in-plane projection direction. Left: m points upward along the line, making an acute theta to n; alpha=90 degrees−theta. Right: m is reversed, making theta obtuse; alpha=theta−90 degrees. The line–plane angle stays the same, giving the absolute dot-product sine formula.
Two schematic source cases share a plane, its normal n, the line and a dashed in-plane projection direction. Left: m points upward along the line, making an acute theta to n; alpha=90 degrees−theta. Right: m is reversed, making theta obtuse; alpha=theta−90 degrees. The line–plane angle stays the same, giving the absolute dot-product sine formula.
Two schematic source cases share a plane, its normal n, the line and a dashed in-plane projection direction. Left: m points upward along the line, making an acute theta to n; alpha=90 degrees−theta. Right: m is reversed, making theta obtuse; alpha=theta−90 degrees. The line–plane angle stays the same, giving the absolute dot-product sine formula.
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