The correct option is C 2^i+2^j+2^k
Given, a vector →v and a unit vector ^n, you can divide the vector →v into two parts →v=→p+→q
where →p and →q are parallel and perpendicular to ^n respectively. Now, the magnitude of →p is given by →p.^n .
Since →q.^n=0, we have,
Since the unit vector in the direction of →a is given by →a|→a|, the component of →v parallel to →a is given by
So, for the given problem, the component that we get is