vector fields a and b are given as following mathbfar sin theta cos em

Question

Vector fields A and B are given as following. \mathbf{A}=r \sin (\theta) \cos (\emptyset) \mathbf{a}_{\boldsymbol{r}}+\sin (\emptyset) \boldsymbol{a}_{\theta}-r \boldsymbol{a}_{\boldsymbol{\phi}} \mathbf{B}=\cos (\theta) \mathbf{a}_{\boldsymbol{r}}+\sin (\emptyset) \boldsymbol{a}_{\theta}+2 r^{2} \boldsymbol{a}_{\boldsymbol{\phi}} ] Formulate and calculate the component of A along the direction of B at P\left(1, \frac{\pi}{3}, \frac{3 \pi}{4}\right) \text { Calculate the angle between } \mathbf{A} \text { and } \mathbf{x} \text {-axis at } P\left(1, \frac{\pi}{3}, \frac{3 \pi}{4}\right) c) [10 pts] Explain your solutions in part (a) and (b) verbally with your own word,(i.e. write at least couple of sentences to explain your solution for each part). Please use your own wording and be explanatory.