A vector of magnitude 6 units makes equal makes angles from `OX-,OY-` and `OZ`-axes. Find the vector.

Explanation

Let vector is `vecr`.
This makes equal angles from `OX-,OY` and `OZ-`axes.
`:. l = m = n`
Now from `l^(2) = m^(2) + n^(2) = 1`
`l^(2) + l^(2) + l^(2) = 1 rArr 3l^(2)= 1`
`rArr l = +- (1)/(sqrt(3))`
`:. vecr=|vecr|.(lhati+lhat j+lhatk)`
`= 6(+-(1)/(sqrt(3))hati+-(1)/(sqrt(3))hatj+-(1)/(sqrt(3))hatk)`
`= 2sqrt(3) (+- hati+- hatj+-hatk)`