A vector v is equally inclined to the X-axis, Y-axis and Z-axis respectively the dirction cosines are

Options

A. `lt (1)/(sqrt3),(1)/(sqrt3),(1)/(sqrt3)gt`
B. `lt -(1)/(sqrt3), -(1)/(sqrt3), -(1)/(sqrt3)gt`
C. `lt (1)/(sqrt3), (1)/(sqrt3), (1)/(sqrt3)gt or lt -(1)/(sqrt3), -(1)/(sqrt3), -(1)/(sqrt3)gt`
D. None of the above

Answer

C

Explanation

Let the vecto v make an angle `alpha` with each of the three axes, then diractin consine of v are
`lt cos alpha, cos alpha, cos alphagt`
Also, `cos ^(2)alpha +cos ^(2)alpha+cos ^(2)alpha=1`
`impliescos ^(2)alpha =1//3`
`impliescos alpha =pm(1)/(sqrt3)`
Hence, direction cosine of v are
`lt (1)/(sqrt3),(1)/(sqrt3), (1)/(sqrt3)gt`
or `lt-(1)/(sqrt3), -(1)/(sqrt3),-(1)/(sqrt3)gt`