If `vecr` is a vector of magnitude 21 and has direction ratios proportional to 2,-3,6 then `vecr` is equal to

Options

A. `6hati+9hatj-18hatk`
B. `6hati-9hatj-18hatk`
C. `6hati-9hatj+18hatk`
D. none of these

Answer

C

Explanation

Reall that if the direction ratios of a vector are proportional to `a,b,c` then its direction cosines are
`+-a/(sqrt(a^(2)+b^(2)+c^(2))),+-b/(sqrt(a^(2)+b^(2)+c^(2))),+-c/(sqrt(a^(2)+b^(2)+c^(2)))`
Therefore, direction cosines of `vecr` are
`+-2/(sqrt(2^(2)+(-3)^(2)+6^(2))),+-(-3)/(sqrt(2^(2)+(-3)^(2)+6^(2))),+-6/(sqrt(2^(2)+(-3)^(2)+6^(2)))`
Since `vecr` makes an acute angle with x-axis.
`:.cos alpha gt0` i.e `l gt0`
So direction cosines of `vecr` are `2/7,-3/7,6/7`
`:.vecr=21(2/7hati-3/7hatj+6/7hatk) [ :' vecr=|vecr|(lhati+mhatj+nhatk)]`
`impliesvecr=6hati-9hatj+18hatk`.