Obtain the component of vector A=2i+3j in the direction of vector i+j.
Let,
A = 2i + 3j
B = i + j
Therefore,
|A| = (22 + 32)1/2 = 131/2
|B| = (12 + 12)1/2 = 21/2
A.B = (2i + 3j).( i + j) = 2 + 3 = 5
Suppose θ is the angle between the vectors. The component of A along B is A cosθ.
Now,
A.B = AB cosθ
=> A cosθ = (A.B)/B
=> A cosθ = 5/(21/2) ≈ 3.5