Find a unit vector perpendicular to both \vec{a}  and \vec{b}, where \vec{a}= 4\hat{i}-\hat{j}+8\hat{k},\vec{b}= -\hat{j}+\hat{k}\cdot

 

 

 

 
 
 
 
 

Answers (1)

\vec{a}= 4\hat{i}-\hat{j}+8\hat{k}
\vec{b}= -\hat{j}+\hat{k}
Now , \because we know that vector which is \perp ^{r}  to both vector \vec{a} & \vec{b}  is \left ( \vec{a}\times \vec{b} \right )
\vec{a}\times \vec{b}= \begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\ 4 &-1 &8 \\ 0&-1 &1 \end{vmatrix}= \hat{i}\left ( -1+8 \right )-\hat{j}\left ( 4 \right )+\hat{k}\left ( -4 \right )
                                      \Rightarrow 7\hat{i}-4\hat{j}-4\hat{k}
Unit vector = \frac{\vec{a}\times \vec{b}}{\left | \vec{a}\times \vec{b} \right |}= \frac{7\hat{i}-4\hat{j}-4\hat{k}}{\sqrt{49+16+16}}
                   =\frac{7\hat{i}-4\hat{j}-4\hat{k}}{9}                

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