Answer
a) $(-14,13,17).$
b) $(14,-13,-17).$
c) $(0,0,0)$
Work Step by Step
We know that $ai+bj+ck=(a,b,c).$
We know that for a matrix
$
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
$
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
a) $u×v$ is the determinant of the matrix $\begin{bmatrix}
i& j & k \\
3& -2&4\\
1&5 &-3 \\
\end{bmatrix}
$
Thus $u×v=(-14,13,17).$
b) From earlier: $v\times u=-u\times v=-(-14,13,17)=(14,-13,-17)$
c) From earlier $v\times v=(0,0,0)$ for any vector $v$.
