For example, given the 2D vector u=[2,3], how would I determine the vector that is perpendicular to u?
Also, given the 3D vector v=[3,6,1], how would I determine the vector that is perpendicular to u>
Asked
Active
Viewed 59 times
0
-
A vector that is perpendicular is one who when doing the dot product (inner product) with your vector results in zero. You can describe this as a matrix equation, just like you can describe many other things in linear algebra as matrix equations, and the same techniques used to solve other matrix equations work here as well. – JMoravitz Apr 03 '21 at 02:00
-
the vector perpendicular to $u$? A moments thought about the geometry here should convince you that there are infinitely many vectors perpendicular to $u$ in two dimensions, and a two-dimensional family of answers in three dimensions. – Gerry Myerson Apr 03 '21 at 02:02
-
You will find that in $\Bbb R^n$, given a nonzero vector $v$ there is an entire $(n-1)$-dimensional subspace of $\Bbb R^n$ perpendicular to $v$. There is more than just one vector perpendicular to it... so the phrasing "how would I determine the vector..." is improper as the usage of "the" would imply that you think there is only one. – JMoravitz Apr 03 '21 at 02:02