# E and F are vector fields given by E=2xa_x +a_y +yza_z and F=xya_x -y^2 a_y +xyza_z. Determine (a)|E| at (1,2,3)

E and F are vector fields given by $E=2x{a}_{x}+{a}_{y}+yz{a}_{z}$ and $F=xy{a}_{x}-{y}^{2}{a}_{y}+xyz{a}_{z}$.
Determine:
(a)|E| at (1,2,3)
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sweetwisdomgw
a) $E=2x{a}_{x}+{a}_{y}+yz{a}_{z}$
we assume that the vector ${a}_{x,y,z}$ are mutually perpendicular
in x,y,z directions respectively (i.e ${a}_{x}\ast {a}_{y}=0;{a}_{x}\ast {a}_{z}=0$)
E at (1,2,3) is, $2{a}_{x}={a}_{y}+6{a}_{z}$
Then $|E|=\sqrt{E.E}=\sqrt{\left(2{a}_{x}+{a}_{y}+6{a}_{z}\right).\left(2{a}_{x}+{a}_{y}+6{a}_{z}\right)}$
$=\sqrt{4+1+36}=\sqrt{41}$