1.

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

Answer»

`3 hat(i)+hat(J)-3hat(K)`
`3hat(i)-hat(j)+3hat(k)`
`3hat(i)+hat(j)+3hat(k)`
`-3hat(i)+hat(j)+3hat(k)`

Solution :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`


Discussion

No Comment Found

Related InterviewSolutions