From a8de6477af4cc8ee964138f59c984589e8bab4ed Mon Sep 17 00:00:00 2001 From: Alvie Rahman Date: Wed, 2 Mar 2022 01:34:03 +0000 Subject: [PATCH] fix vector formatting issue --- uni/mmme/1026_maths_for_engineering/vectors.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/uni/mmme/1026_maths_for_engineering/vectors.md b/uni/mmme/1026_maths_for_engineering/vectors.md index edf948c..1bae219 100755 --- a/uni/mmme/1026_maths_for_engineering/vectors.md +++ b/uni/mmme/1026_maths_for_engineering/vectors.md @@ -248,7 +248,7 @@ $$\frac{x-x_0}{d_1} = \frac{y-y_0}{d_2} = \frac{z-z_0}{d_3}$$ A *plane* can be defined by specifying either: - three points (as long as they're not in a straight line) -- a point on the plne and two directions (useful for a parametric form) +- a point on the plane and two directions (useful for a parametric form) - specifying a point on the plane and the normal vector to the plane #### Specifying a Point and a Normal Vector @@ -263,7 +263,7 @@ $$(\pmb r - \pmb a) \cdot \pmb n = 0$$ So the *vector equation* of the plane is -$$\pmb r \cdot \pmb n = \pmb a \cdot n = d$$ +$$\pmb r \cdot \pmb n = \pmb a \cdot \pmb n = \pmb d$$ where $\pmb r = (x, y, z)$ and the vectors $\pmb a$ and $\pmb n$ are known. @@ -291,6 +291,7 @@ and so the equation of the plane is $$(\pmb r - \pmb a)\cdot((\pmb c - \pmb a)\times(\pmb c - \pmb b)) = 0$$ + #### The Angle Between Two Planes ... is the same as the angle between their normal vectors