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If vec(A)=2hat(i)+3hat(j)-hat(k) and vec...

If `vec(A)=2hat(i)+3hat(j)-hat(k)` and `vec(B)=-hat(i)+3hat(j)+4hat(k)`, then find the projection of `vec(A)` on `vec(B)`.

A

`3/(sqrt(3))`

B

`3/(sqrt(26))`

C

`sqrt(3/(26))`

D

`sqrt(3/(13))`

Text Solution

Verified by Experts

The correct Answer is:
B
`|vec(A)|=sqrt(2^(2)+3^(2)+(-1)^(2))=sqrt(4+9+1)= sqrt(14)`
`|vec(B)|=sqrt((-1)^(2)+3^(2)+4^(2))=sqrt(1+9+16)=sqrt(26)`
`vec(A).vec(B)= 2(-1)+3xx3+(-1)(4)=3`
The projection of `vec(A) on vec(B)=(vec(A).vec(B))/(|vec(B)|)= 3/(sqrt(26))`
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