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avatar+221 

 

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
avatar+31320 
+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
avatar+111602 
+1

Thanks Alan, that sure made it easy laugh

 Oct 31, 2020

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