Find \left | \vec{a} \times \vec{b}\right |,\: if\: \vec{a}= 2\hat{i}+\hat{j}+3\hat{k}\, and\: \vec{b}= 3\hat{i}+5\hat{j}-2\hat{k}.

 

 

 

 
 
 
 
 

Answers (1)

given: \vec{a}= 2\hat{i}+\hat{j}+3\hat{k}
           \vec{b}= 3\hat{i}+5\hat{j}-2\hat{k}
Then \vec{a}\times \vec{b}= \begin{bmatrix} \hat{i}& \hat{j} &\hat{k} \\ 2& 1 &3 \\ 3&5 &-2 \end{bmatrix}
= \hat{i}\left ( -2-15 \right )-\hat{j}\left ( -4-9 \right )+\hat{k}\left ( 10-3 \right )
=-17\hat{i}+13\hat{j}+7\hat{k}
\left | \vec{a}\times \vec{b} \right |= \sqrt{\left ( -17 \right )^{2}+\left ( 13 \right )^{2}+\left ( 7 \right )^{2}}
              = \sqrt{289+169+49}= \sqrt{507}

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