Question

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)`.

Answer 1

`|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/sqrt26`