Question

Given two vector A = 5i, B = 3j. Direction of (B x A) is ?

Answer 1

Task. Given two vector $\mathrm{A} = 5\mathrm{i}$, $\mathrm{B} = 3\mathrm{j}$. What is the direction of the cross product $[B \times A]$?

Solution. Since $[j \times i] = -k$, we obtain that $[B \times A] = -15k$.

We can produce direct calculation. We have that $A = (5,0,0) = 5i$, $B = (0,3,0) = 3j$. Then $[B \times A]$ has the following coordinates:

$$\begin{aligned} [B \times A] &= \left( \left| \begin{array}{cc} 3 & 0 \\ 0 & 0 \end{array} \right|, \left| \begin{array}{cc} 0 & 0 \\ 0 & 5 \end{array} \right|, \left| \begin{array}{cc} 0 & 3 \\ 5 & 0 \end{array} \right| \right) \\ &= (3 * 0 - 0 * 0, 0 * 5 - 0 * 0, 0 * 0 - 3 * 5) \\ &= (0, 0, -15) = -15k. \end{aligned}$$

Answer. $[B \times A] = -15k$.