Question

For the following three vectors, what is 2 . c . ?A × B | ? A 3.00i 3.00j 3.00k B 4.00i+ 3.00j+ 3.00k C = 7.00;-9.00/ Number Units

Answer 1

$\\\left ( 2\vec{A} \times \vec{B}\right )=\begin{vmatrix} \hat{i} & \hat{j} & \hat{k}\\ 6.00 & 6.00 & -6.00\\ -4.00 & 3.00 & 3.00 \end{vmatrix}\\\\ \left ( 2\vec{A} \times \vec{B}\right )=\hat{i}((6\times 3)-(-6\times 3))-\hat{j}((6\times 3)-(-4\times -6))+\hat{k}((6\times 3)-(-4\times 6))\\\\ \left ( 2\vec{A} \times \vec{B}\right )=\hat{i}(18+18)-\hat{j}(18-24)+\hat{k}(18+24)\\\\ \left ( 2\vec{A} \times \vec{B}\right )=36\;\hat{i}+6\;\hat{j}+42\hat{k}\\\\ 2\cdot C\cdot \left ( 2\vec{A} \times \vec{B}\right )=2\cdot (7.00\;\hat{i}-9\;\hat{j})\cdot (36\;\hat{i}+6\;\hat{j}+42\hat{k})\\\\ 2\cdot C\cdot \left ( 2\vec{A} \times \vec{B}\right )=2(\;(7\times 36)-(9 \times 6))=2(252-54)=396\;$