The velocity of a particle is `v=6hat(i)+2hat(j)-2hat(k).` The component of the velocity parallel to vector `a=hat(i)+hat(j)+hat(k)` in vector form is

Options

A. `6hat(i)+2hat(j)+2hat(k)`
B. `2hat(i)+2hat(j)+2hat(k)`
C. `hat(i)+hat(j)+hat(k)`
D. `6hat(i)+2hat(j)-2hat(k)`

Answer

B

Explanation

(b) Magnitude of component of v along a
`=(v.a)/(a)=(6+2-2)/(sqrt(3))=2sqrt(3)`
`"Now "hat(a)=(hat(i)+hat(j)+hat(k))/(sqrt(3))`
:.Component in vector form
`=2sqrt(3)hat(a)`
`=(2hat(i)+2hat(j)+2hat(k))`