if the component of A along B is same as that of component of B along A then angle between A and B is

To find the angle between vector A and vector B when the component of A along B is the same as the component of B along A, we can use the dot product of two vectors.

Given A and B, we can find their dot product using the formula:

A · B = |A| |B| cosθ

where A · B is the dot product, |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.

Now, let's find the dot product of A and B and equate it to the product of their magnitudes multiplied by the cosine of the angle between them:

A · B = |A| |B| cosθ

Since the component of A along B is the same as the component of B along A, we have:

A · B = B · A

Applying this to the equation, we get:

B · A = |A| |B| cosθ

Since A · B = B · A, we can conclude that |A| |B| cosθ = |A| |B| cosθ, which is always true.

So, the equation |A| |B| cosθ = |A| |B| cosθ holds for any angle θ between A and B. Thus, there is no specific angle between A and B when the component of A along B is the same as the component of B along A.