fix vector formatting issue
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@ -248,7 +248,7 @@ $$\frac{x-x_0}{d_1} = \frac{y-y_0}{d_2} = \frac{z-z_0}{d_3}$$
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A *plane* can be defined by specifying either:
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- three points (as long as they're not in a straight line)
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- a point on the plne and two directions (useful for a parametric form)
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- a point on the plane and two directions (useful for a parametric form)
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- specifying a point on the plane and the normal vector to the plane
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#### Specifying a Point and a Normal Vector
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@ -263,7 +263,7 @@ $$(\pmb r - \pmb a) \cdot \pmb n = 0$$
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So the *vector equation* of the plane is
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$$\pmb r \cdot \pmb n = \pmb a \cdot n = d$$
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$$\pmb r \cdot \pmb n = \pmb a \cdot \pmb n = \pmb d$$
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where $\pmb r = (x, y, z)$ and the vectors $\pmb a$ and $\pmb n$ are known.
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@ -291,6 +291,7 @@ and so the equation of the plane is
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$$(\pmb r - \pmb a)\cdot((\pmb c - \pmb a)\times(\pmb c - \pmb b)) = 0$$
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#### The Angle Between Two Planes
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... is the same as the angle between their normal vectors
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