Given : `vec A =2hati +3hatj and vec B = hati +hatj`. What is the component of vector `vec A` along the vector `vec B` ?

Options

A. `(7)/(sqrt(2))`
B. `(5)/(sqrt(2))`
C. `(3)/(sqrt(2))`
D. `(1)/(sqrt(2))`

Answer

B

Explanation

The component of vector `vec A" on "vec B" is "(vec A cdot vec B)/(|B|)`.
`therefore` In this case, `vec A cdot vec B =(2hati + 3hatj) cdot (hati+hatj)`
`=2+3=5`
and `|B| = sqrt (1^(2) +1^(2)) = sqrt (2)`
`therefore (vec A cdot vec B)/(|B|) =(5)/(sqrt(2))`