Obtain the component of vector **A**=2*i+3j *in the direction of vector *i+j*.

Let,

**A** = 2*i* + 3*j*

**B** = *i* + *j*

Therefore,

|**A**| = (2^{2} + 3^{2})^{1/2} = 13^{1/2}

|**B**| = (1^{2} + 1^{2})^{1/2} = 2^{1/2}

**A.B** = (2*i* + 3*j*).(* 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/(2^{1/2}) ≈ 3.5

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