0
$\begingroup$

On a $3$ dimensional plane:

Given that two vectors $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ are known and that each of these vectors belong to two separate straight lines intersecting each other at $(0,0,0)$

What formula can be used to calculate the angle formed by the intersecting lines?

$\endgroup$
2
$\begingroup$

If you have two vectors $\mathbf v$ and $\mathbf w$ that both start from the origin, their dot product is $$ \mathbf v\cdot\mathbf w = \|\mathbf v\| \|\mathbf w \| \cos(\theta) $$ where $\theta$ is the angle between them, and $\|\mathbf v\|$ is the magnitude of $\mathbf v$.

$\endgroup$
2
$\begingroup$

You already know they intersect and each belong to a straight line going through $(0,0,0)$, so you can safely assume their cartesian coordinates as originating from $(0,0,0)$.

Now you just need to build the dot product and solve for your angle and you're done!

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.