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math: add instructions for direction of vectors

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eggy 2020-09-22 21:34:59 -04:00
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docs/sph3u7.md
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@ -207,6 +207,18 @@ $$
(a_{x}, a_{y}) - (b_{x}, b_{y}) = (a_{x} - b_{x}, a_{y} - b_{y}) (a_{x}, a_{y}) - (b_{x}, b_{y}) = (a_{x} - b_{x}, a_{y} - b_{y})
$$ $$
The length of resultant vector can then be found using the Pythagorean theorem.
$$
|\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 ### 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. 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.