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.