A vector `vecr` is inclined at equal angles to the three axes. If the magnitude of `vecr` is `2sqrt3` units, then find the value of `vecr`.

Explanation

We have `|vecr|=2sqrt3`
Since, `vecr` is equally inclined ot the three axes, `vecr` so dircetion cosines of the unit vector `vecr` will be same.i.e., l=m=n.
We know that,
`l^(2)+m^(2)+n^(2)=1`
`impliesl^(2)+l^(2)+l^(2)=1`
`impliesl^(2)=(1)/(3)`
`impliesl=+-((1)/(sqrt3))`
So, `hatr=+-(1)/(sqrt3)hati+-(1)/(sqrt3)hatj+-(1)/(sqrt3)hatk`
`:.vecr=vecr|vecr|" "[:'vecr=(vecr)/(vec|r|)]`
`=[+-(1)/(sqrt3)hati+-(1)/(sqrt3)hatj+-(1)/(sqrt3)hatk]2sqrt3" "[:'|vecr|=2sqrt3]`
`=+-2hati+-2hatj+-2hatk=+-2(hati+hatj+hatk)`