Suppose-one-is-given-two-vector-field-A-and-B-in-region-of-space-such-that-A-x-y-z-4xi-zj-y-2-z-2-k-B-x-y-z-yi-3j-yzk-Find-C-x-y-z-if-C-A-B-Also-prove-that-C-x-y-z-is-perpendi

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Question Number 18377 by tawa tawa last updated on 19/Jul/17

$$\mathrm{Suppose}\mathrm{one}\mathrm{is}\mathrm{given}\mathrm{two}\mathrm{vector}\mathrm{field}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{in}\mathrm{region}\mathrm{of}\mathrm{space}\mathrm{such}\mathrm{that},$$$$\mathrm{A}(\mathrm{x},\mathrm{y},\mathrm{z})=4\mathrm{xi}+\mathrm{zj}+{\mathrm{y}}^2{\mathrm{z}}^2\mathrm{k}$$$$\mathrm{B}(\mathrm{x},\mathrm{y},\mathrm{z})=\mathrm{yi}+3\mathrm{j}-\mathrm{yzk}$$$$\mathrm{Find}:\mathrm{C}(\mathrm{x},\mathrm{y},\mathrm{z})\mathrm{if}\mathrm{C}=\mathrm{A}\wedge \mathrm{B}$$$$\mathrm{Also}\mathrm{prove}\mathrm{that},\mathrm{C}(\mathrm{x},\mathrm{y},\mathrm{z})\mathrm{is}\mathrm{perpendicular}\mathrm{to}\mathrm{A}(\mathrm{x},\mathrm{y},\mathrm{z})$$

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