How do you solve this:
How do I find how long the red line is?
$\endgroup$2 Answers
$\begingroup$you can find the angle $t$ between your $m$ and the unit vector $d.$ it is given by $\cos t = \dfrac{m.t}{|m|}$ the component in the direction orthogonal has length $|m|\sin t.$
$\endgroup$ $\begingroup$assuming vector $\vec{d}$ and $\vec{q}$ have unite length.
$\vec{m}_q$ is projection of $\vec{m}$ on $\vec{q}$:
$$\vec{m}_q=(\vec{m}\cdot \vec{q})\vec{q}$$ $$|\vec{red}|=|\vec{m}-(\vec{m}\cdot \vec{q})\vec{q}|$$
$\endgroup$ 2
