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  • Please help! The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction cosines of the vector are

The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction cosines  of the vector are

  • Option 1)

    \frac{6}{5},\frac{-3}{5},\frac{2}{5}

  • Option 2)

    \frac{6}{7},\frac{-3}{7},\frac{2}{7}

  • Option 3)

    \frac{-6}{7},\frac{-3}{7},\frac{2}{7}

  • Option 4)

    6,-3,2

 

Answers (1)

best_answer

As we learnt in 

Direction Cosines of a Vector -

\cos \alpha, \cos \beta, \cos \gamma are the Direction Cosines. They are denoted by l, m, n, 

- wherein

fig6

 

 Projections are (6,-3,2)

Magnitude =\sqrt{6^{2}+(-3)^{2}+2^{2}}=7

Thus DCs\:are \left(\frac{6}{7},\frac{-3}{7},\frac{2}{7} \right )


Option 1)

\frac{6}{5},\frac{-3}{5},\frac{2}{5}

This solution is incorrect 

Option 2)

\frac{6}{7},\frac{-3}{7},\frac{2}{7}

This solution is correct 

Option 3)

\frac{-6}{7},\frac{-3}{7},\frac{2}{7}

This solution is incorrect 

Option 4)

6,-3,2

This solution is incorrect 

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Plabita

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