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  • A vector  makes angles <img alt="\frac{\pi }{6}, \frac{2\pi }{3} , \fra

A vector \overrightarrow{r} makes angles \frac{\pi }{6}, \frac{2\pi }{3} , \frac{\pi }{2} with positive x, y and z axis respectively then sum of its direction angle is:

Option: 1

\frac{\pi }{3}

 

 

 


Option: 2

\frac{4\pi }{3}


Option: 3

\frac{5\pi }{3}


Option: 4

\frac{7\pi }{3}


Answers (1)

best_answer

As we learn

Direction Angles of a Vectors -

Let \alpha, \beta, \gamma be the angles which vector  \vec{r}makes with the positive directions of the x,y, and z-axis.

- wherein

Fig 6

 

 Here \alpha = \frac{\pi }{6}, \beta =\frac{2\pi }{3}, \gamma =\frac{\pi }{2}

\therefore \alpha + \beta + \gamma =\frac{\pi }{6}+\frac{2\pi }{3}+\frac{\pi }{2} = \frac{4\pi }{3}

\therefore option B

Posted by

avinash.dongre

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