A vector ` vec r` is inclined at equal to `O X ,O Ya n dO Zdot` If the magnitude of ` vec r` is 6 units, find ` vec rdot`

Options

A. `sqrt(3)(+-hati+-hatj+-hatk)`
B. `2sqrt(3)(+-hati+-hatj+-hatk)`
C. `6(+-hati+-hatj+-hatk)`
D. none of these

Answer

B

Explanation

Let `l,m,n` be the direction cosines of `vecr` which is equally inclied to the coordinate axes. The,
`:. L=m=n+-1/(sqrt(3))`
Hence `vecr=|vecr+(lhati+mhatj+nhatk)`
`impliesvecr=6{+-1/(sqrt(3))hati+-1/(sqrt(3))hatj+-1/(sqrt(3))hatk}=2sqrt(3)(+-hati+-hatj+-hatk)`