The discussion centers on the derivation of the term \( A_x \) from the product rule in vector calculus, specifically in the context of the formula for vector components. Participants clarify that \( A_x \) represents the x-component of a vector \( \vec A \), expressed as \( A_x = \vec A \cdot \hat i \). The confusion arises from the exclusion of the y and z components, which are not relevant when focusing solely on the x-direction. The use of i-hat, j-hat, and k-hat notation is essential for understanding vector representation in this context.
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who are working with vector calculus and need clarification on vector component notation and derivations.
Yeah I had a guess what assumed that was it but why is it included and not y or z aswell? Maybe I am missing an i hat which will get rid of the j and z hat cos of the dot product?anuttarasammyak said:
I’m not sure how to type maths in here but I think you have just helped me crack it, because it’s in the x direction only we ignore y hat and z hat, then In the product rule you’re left with the extra x.PeroK said:
By definition $$\vec A = A_x \hat i + A_y \hat j + A_z \hat k$$This can also be expressed as:$$A_x = \vec A \cdot \hat i$$bigmike94 said: