If `vecb ne 0`, then every vector `veca` can be written in a unique manner as the sum of a vector `veca_(p)` parallel to `vecb` and a vector `veca_(q)` perpendicular to `vecb`. If `veca` is parallel to `vecb` then `veca_(q)`=0 and `veca_(q)=veca`. The vector `veca_(p)` is called the projection of `veca` on `vecb` and is denoted by proj `vecb(veca)`. Since proj`vecb(veca)` is parallel to `vecb`, it is a scalar multiple of the vector in the direction of `vecb` i.e.,
proj `vecb(veca)=lambdavecUvecb" " (vecUvecb=(vecb)/(|vecb|))`
The scalar `lambda` is called the componennt of `veca` in the direction of `vecb` and is denoted by comp `vecb(veca)`. In fact proj `vecb(veca)=(veca.vecUvecb)vecUvecb` and comp `vecb(veca)=veca.vecUvecb`.
If `veca=-2hatj+hatj+hatk` and `vecb=4hati-3hatj+hatk` then proj `vecb(veca)` is

Options

A. `(1)/(13)(-3hati+hatj+9hatk)`
B. `(1)/(13)(-3hati-hatj+4hatk)`
C. `(2)/(13)(-3hati+hatj+9hatk)`
D. `-(2)/(13)(3hati+hatj-9hatk)`

Answer

3