From 834ee6b5f3f30ea6cfaa8393721693cef0280100 Mon Sep 17 00:00:00 2001 From: eggy Date: Tue, 22 Sep 2020 21:34:59 -0400 Subject: [PATCH] math: add instructions for direction of vectors --- docs/sph3u7.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/docs/sph3u7.md b/docs/sph3u7.md index 1d4a195..aebd023 100644 --- a/docs/sph3u7.md +++ b/docs/sph3u7.md @@ -207,6 +207,18 @@ $$ (a_{x}, a_{y}) - (b_{x}, b_{y}) = (a_{x} - b_{x}, a_{y} - b_{y}) $$ +The length of resultant vector can then be found using the Pythagorean theorem. + +$$ +|\vec{c}|=\sqrt{(a_{x}+b_{x})^2 + (a_{y}+b_{y})^2} +$$ + +To find the resultant direction, use inverse tan to calculate the angle of the vector using the lengths of its components. + +$$ +\vec{c}_{direction} = \tan^{-1} \frac{c_y}{c_x} +$$ + ### Multiplying vectors and scalars The product of a vector multiplied by a scalar is a vector with a magnitude of the vector multiplied by the scalar with the same direction as the original vector.