Let ` vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k` be three vectors. A vector ` vec v` in the plane of ` vec aa n d vec b ,` whose projection on ` vec c` is `1/(sqrt(3))` is given by ` hat i-3 hat j+3 hat k` b. `-3 hat i-3 hat j+3 hat k` c. `3 hat i- hat j+3 hat k` d. ` hat i+3 hat j-3 hat k`

Options

A. `3 hat(i)+hat(j)-3hat(k)`
B. `3hat(i)-hat(j)+3hat(k)`
C. `3hat(i)+hat(j)+3hat(k)`
D. `-3hat(i)+hat(j)+3hat(k)`

Answer

B

Explanation

Here, `(v.c)/(|c|) = 1/(sqrt(3))`
`rArr (v.c)/(sqrt(1+1+1)) = 1/(sqrt(3))`
`rArr (v.c)/(sqrt(3)) = 1/(sqrt(3)) rArr v.c = 1`
`rArr v.(hati-hatj -hatk) = 1 "….."(i)`
we get from option (b) `v=3 hati-hatj+3hatk`
` v.c (3hati -hatj+3hatk)`
`=3+1-3=1`
which satisfies Eq. 9i)
`v=3hati-hatj+3hatk`