Question

3.35 Transform the following vectors into spherical coordinates and then evaluate them at the indicated points: \text { (a) } \mathbf{A}=\hat{\mathbf{x}} y^{2}+\hat{\mathbf{y}} x z+\mathbf{z} 4 \text { at } P_{1}=(1,-1,2) \text { (b) } \mathbf{B}=\hat{\mathbf{y}}\left(x^{2}+y^{2}+z^{2}\right)-\hat{\mathbf{z}}\left(x^{2}+y^{2}\right) \text { at } P_{2}=(-1,0,2) \text {, } \text { (c) } \mathbf{C}=\hat{\mathbf{r}} \cos \phi-\boldsymbol{\phi} \sin \phi+\hat{\mathbf{z}} \cos \phi \sin \phi \text { at } P_{3}=(2 . \pi / 4.2), \text { and } \text { (d) } \mathbf{D}=\hat{\mathbf{x}} y^{2} /\left(x^{2}+y^{2}\right)-\hat{\mathbf{y}} x^{2} /\left(x^{2}+y^{2}\right)+\mathbf{2} 4 \text { at } P_{4}=(1,-1,2)

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