# If a * i=4, then ,what is the value of (axj) * (2j-3k) , where a is a vector

If a.i=4, then ,what is the value of (axj).(2j-3k) , where a is a vector
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yatangije62
$a\cdot i=4$ means that $a=4i+sj+tk$ where s and t are real, and so $a×j=4k-ti$. Now take the dot product with $2j-3k$; I think that pesky t will obligingly vanish.
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Bernard Boyer
$\left(a×\mathbf{j}\right)\cdot \left(2\mathbf{j}-3\mathbf{k}\right)=a\cdot \left(\mathbf{j}×\left(2\mathbf{j}-3\mathbf{k}\right)=a\cdot \left(-3\mathbf{i}\right)=\left(4\mathbf{i}\right)\cdot \left(-3\mathbf{i}\right)=-12$