A recent class assignment involved finding a unit vector perpendicular to a plane, given two unit vectors to start with. The solution given involved using the cross product; I was wondering if such a problem could be solved using a 3x3 matrix (technically, material not yet covered in my class).
How would one use matrices to find a normal unit vector?
0
$\begingroup$
matrices
3d
vector-analysis
1 Answers
1
Yes, it can – if you form the determinant of
$ \pmatrix{u_1&v_1&x_1\\u_2&v_2&x_2\\u_3&v_3&x_3}\;, $
where $u$ and $v$ are the two given unit vectors, the coefficients of $x_1$, $x_2$ and $x_3$ form $u\times v$.