Question

Define A = 5i + 6j - 7k and B = 2i - 4j +2k.

Find |A x B|.

Answer 1

The vector product is given by

$${\bf A\times B}=\begin{vmatrix} {\bf i} & {\bf j }& {\bf k} \\ A_x & A_y &A_z\\ B_x & B_y &B_z \end{vmatrix}$$

$${\bf A\times B}=\begin{vmatrix} {\bf i} & {\bf j }& {\bf k} \\ 5 & 6 &-7\\ 2 & -4 &2 \end{vmatrix}$$

$$=-16{\bf i}-24{\bf j}-32{\bf k}$$

Finally,

$$|{\bf A\times B}|=\sqrt{(-16)^2+(-24)^2+(-32)^2}=43$$