Find a unit vector perpendicular to both the vectors \vec{a}\,\, and\,\, \vec{b}, where \vec{a}= \hat{i}-7\hat{j}+7\hat{k}\:\: and\:\, \vec{b}= 3\hat{i}-2\hat{j}+2\hat{k}.

 

 

 

 
 
 
 
 

Answers (1)

(A)           a= \hat{i}-7\hat{j}+7\hat{k} \: \: b= 3\hat{i}-2\hat{j}+2\hat{k}
                 Let n be the vector perpendicular to a & b
                \vec{n}= \vec{a}\times \vec{b}
         \vec{A}= \begin{vmatrix} \hat{i} & \hat{j} & \hat{k}\\ 1& -7 & 7\\ 3& -2& 2 \end{vmatrix}= 19{\hat{j}}+19{\hat{k}}
        \hat{n}= \frac{19\hat{j}+19\hat{k}}{\sqrt{19^{2}+19^2}}= \frac{1}{\sqrt{2}}\left ( \hat{j} +\hat{k}\right )
       

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