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A vector \overrightarrow{\gamma } is such that \overrightarrow{\gamma } =3\hat{i}-6\hat{j}+2\hat{k} then \cos\alpha + \cos\beta + \cos\gamma equals:

Option: 1

-1/7


Option: 2

-2/7


Option: 3

-4/7


Option: 4

-5/7


Answers (1)

best_answer

As we learn

Direction Cosines of a Vector -

\cos \alpha =\frac{x}{\mid r\mid };\cos \beta =\frac{y}{\mid r\mid };\cos\gamma =\frac{z}{\mid r\mid }

- wherein

fig6

 

 cos\alpha =\frac{3}{\sqrt{49}}=\frac{3}{7}; cos\beta =\frac{-6}{7}; cos\gamma =\frac{2}{7}

     \therefore \cos\alpha+ \cos\beta +\cos\gamma = \frac{-1}{7}

\therefore option A

 

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Sayak

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