The magnitude of the projection of the vector 2\hat{i}+3\hat{j}+\hat{k} on the vector perpendicular to the plane containing the vectors \hat{i}+\hat{j}+\hat{k} and \hat{i}+2\hat{j}+3\hat{k} is :

 

  • Option 1)

    \sqrt{\frac{3}{2}}

  • Option 2)

    \sqrt{6}

  • Option 3)

    \frac{\sqrt{3}}{2}

     

  • Option 4)

    3\sqrt{6}

 

Answers (1)

Normal vector to plane containing vector \hat{i}+\hat{j}+\hat{k}

and \hat{i}+2\hat{j}+3\hat{k} is

\hat{n}=(\hat{i}+\hat{j}+\hat{k})\times(\hat{i}+2\hat{j}+3\hat{k})

\hat{n}=\hat{i}-2\hat{j}+\hat{k}

Projection of 2\hat{i}+3\hat{j}+\hat{k} on \hat{n}

=\left | \frac{(2\hat{i}+3\hat{j}+\hat{k})(\hat{i}-2\hat{j}+\hat{k})}{\sqrt{1+4+1}} \right |

=\frac{3}{\sqrt{6}}=\sqrt{\frac{3}{2}}


Option 1)

\sqrt{\frac{3}{2}}

Option 2)

\sqrt{6}

Option 3)

\frac{\sqrt{3}}{2}

 

Option 4)

3\sqrt{6}

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