Answer
a) $v \times w =i -j -k$
b) $v \times w=-i+j+k$
c) $v \times v = 0$
d) $w \times w =0$
Work Step by Step
Supposes that the two vectors can be represented as: $v=xi+yj+zk$ and $w=pi+qj+rk$, then their cross product of such vectors can be obtained in the form of determinate as :
$ v \times w=\begin{vmatrix} i & j & k \\ x & y & z \\ p & q & r \\ \end{vmatrix}$
a) $det =v \times w =[(1)(1)-(0)(1)] i -j [(1)(1) - (0)(2)]+k [(1)(1) -(1) (2)]=i -j -k$
b) Since, a cross or vector product is not commutative. So we can write as: $v \times w= -w \times v$
So, $v \times w=-i+j+k$
c) We know that for the two mutually perpendicular vectors, we have: $v \times v = 0$.
d) We know that for the two mutually perpendicular vectors, we have: $w \times w =0$.
