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

  • 86

Component of A on B = A.B/b. Here b is magnitude of vector B. thus answer is (2i + 3j)/1.414

  • -8
What are you looking for?