+0

0
108
3
+226

Let a,b,c be vectors such that $$\mathbf{a} \times \mathbf{b} = \begin{pmatrix} -1 \\- 1 \\ -1 \end{pmatrix}, \mathbf{a} \times \mathbf{c} = \begin{pmatrix} -1 \\ 2 \\ 1 \end{pmatrix}, \text{ and } \mathbf{b} \times \mathbf{c} = \begin{pmatrix} 0 \\ 2 \\ 3 \end{pmatrix}$$
Then evaluate $$(\mathbf{b} + \mathbf{c})\times \mathbf{b}, \mathbf{a}\times(\mathbf{b} + 4 \mathbf{a}), (\mathbf{a} + \mathbf{b} + \mathbf{c})\times \mathbf{a}$$

Oct 30, 2020

#2
+31698
+3

For cross products we have the following

a x a = 0  (simiarly for b x b etc)

a x b = - b x a   etc.

(b + c) x a = b x+  c x a   =   -x b  -  a x c    etc.

Can you take it from here?

Oct 30, 2020
#3
+112499
+1

Thanks Alan, that sure made it easy

Oct 31, 2020