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

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`