From a5e865c29d9c7c6d723b035506cede634e59d132 Mon Sep 17 00:00:00 2001 From: Alvie Rahman Date: Sun, 20 Feb 2022 14:40:12 +0000 Subject: [PATCH] add section angle between vectors --- uni/mmme/1026_maths_for_engineering/vectors.md | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/uni/mmme/1026_maths_for_engineering/vectors.md b/uni/mmme/1026_maths_for_engineering/vectors.md index e91ddf5..edf948c 100755 --- a/uni/mmme/1026_maths_for_engineering/vectors.md +++ b/uni/mmme/1026_maths_for_engineering/vectors.md @@ -187,6 +187,13 @@ which has a magnitude and direction given by the line $\overrightarrow{OP}$. A point $(x, y, z)$ in Cartesian space has the position vector $r = x\pmb i + y\pmb j + z\pmb k$. +## Angle Between Vectors + +By rearranging the [dot product equation](#the-scalar-product-inner-product-dot-product) you can get +an equation to find the angle, $\theta$, between two vectors: + +$$\cos\theta = \frac{\pmb a \cdot \pmb b}{|\pmb a||\pmb b|} = \frac{a_1b_1 + a_2b_2 + a_3b_3}{|\pmb a ||\pmb b|}$$ + # Applications of Vectors ## Application of Vectors to Geometry