Question #212210

Given A= i+2j+3k and B= 2i+j-k, find AxB


1
Expert's answer
2021-06-30T16:53:42-0400
A×B=ijk123211A\times B=\begin{vmatrix} i & j & k \\ 1 & 2 & 3 \\ 2 & 1 & -1 \end{vmatrix}

=i2311j1321+k1221=i\begin{vmatrix} 2 & 3 \\ 1 & -1 \end{vmatrix}-j\begin{vmatrix} 1 & 3 \\ 2 & -1 \end{vmatrix}+k\begin{vmatrix} 1 & 2 \\ 2 & 1 \end{vmatrix}

=i(23)j(16)+k(14)=i(-2-3)-j(-1-6)+k(1-4)

=5i+7j3k=-5i+7j-3k


A×B=5i+7j3kA\times B=-5i+7j-3k



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