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

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 perpendicular to A(x,y,z)

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

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