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(Solved): Double Check Please Find the cross product \( \mathbf{a} \times \mathbf{b} \). \[ \mathbf{a}=\langle ...



Double Check Please

Find the cross product \( \mathbf{a} \times \mathbf{b} \).
\[
\mathbf{a}=\langle 5,4,-3\rangle, \quad \mathbf{b}=\langle 2,-1
Find the cross product \( \mathbf{a} \times \mathbf{b} \). \[ \mathbf{a}=\langle 5,4,-3\rangle, \quad \mathbf{b}=\langle 2,-1,1\rangle \] Verify that it is orthogonal to both \( \mathbf{a} \) and \( \mathbf{b} \). \[ \begin{array}{l} (\mathbf{a} \times \mathbf{b}) \cdot \mathbf{a}= \\ (\mathbf{a} \times \mathbf{b}) \cdot \mathbf{b}= \end{array} \]


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Solution: Given a=?5,4,?3?, b=?2,?1,1? it can be written as a?=5i^+4j^?3k^ , b?=2i^?j^+k^ a?×b?=det([i^j^k^54?32?11]) =i^(4?3)?j^(5+6)+k^(?5?8) a?×b?=
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