What is the component of `(3hati+4hatj)` along `(hati+hatj)` ?

Options

A. `(1)/(2)(hatj+hati)`
B. `(3)/(2) (hatj+hati)`
C. `(5)/(2)(hatj+hati)`
D. `(7)/(2)(hatj+hati)`

Answer

4

Explanation

Component of `vecA` along `vecB = A cos theta = (vecA*vecB)/(B)`
in vector form `= ((vecA*vecB)/(B))hatB= ((veca*vecB)/(B^(2)))vecB`
`vecA*vecB= (3hati+ 4hatj)*(hati+hatj)=7`
`B^(2) = (sqrt(1^(2)+ 1^(2)))^(2)= 2`
thus required component is `= (7)/(2) (hati+hatj)`