Answer
a) $(5,-3,-1).$
b) $(-5,3,1).$
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 \\
1& 2&-1\\
1&1 &2 \\
\end{bmatrix}
$
Thus $u×v=(5,-3,-1).$
b) From earlier: $v\times u=-u\times v=-(5,-3,-1)=(-5,3,1)$
c) From earlier $v\times v=(0,0,0)$ for any vector $v$.
