The component of vector `A= 2hat(i)+3hat(j)` along the vector `hat(i)+hat(j)` is

Options

A. `5`
B. `5//sqrt(2)`
C. `10sqrt(2)`
D. `2 sqrt(5)`

Answer

B

Explanation

Scalar component of `vec(A) along vec(B)` is
`|vec(A)| cos theta = |vec(A)| (vec(A). vec(B))/(|vec(A)| |vec(B)|) = vec(A) . (vec(B))/(|vec(B)|) = vec(A) . hat(B)`
` hat(B) = (vec(B))/(|vec(B)|) = ( i + j)/(sqrt( 1 + 1)) = (1)/(sqrt(2)) ( i + j)`
`vec(A) . hat(B) = ( 2 i + 3 j) . (1)/(sqrt(2))( i + j) = ( 2 + 3)/(sqrt(2)) = (5)/(sqrt(2))`