Suppose
$\vec { F } ( x , y , z ) = - 6 x ^ { 2 } \vec { i } + 12 y ^ { 3 } \vec { j }$
Find a function f(x, y, z) of three variables with the property that the vectors in $\vec { F }$ on a level surface of f (x, y, z) are perpendicular to the level surface of f(x, y, z) at each point.

Question

Suppose
$\vec { F } ( x , y , z ) = - 6 x ^ { 2 } \vec { i } + 12 y ^ { 3 } \vec { j }$
Find a function f(x, y, z) of three variables with the property that the vectors in $\vec { F }$ on a level surface of f (x, y, z) are perpendicular to the level surface of  f(x, y, z) at each point.

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The Answer of Suppose
$\vec { F } ( x , y , z ) = - 6 x ^ { 2 } \vec { i } + 12 y ^ { 3 } \vec { j }$
Find a function f(x, y, z) of three variables with the property that the vectors in $\vec { F }$ on a level surface of f (x, y, z) are perpendicular to the level surface of  f(x, y, z) at each point.

Suppose F⃗(x,y,z)=−6x2i⃗+12y3j⃗\vec { F } ( x , y , z ) = - 6 x ^ { 2 } \vec { i } + 12 y ^ { 3 } \vec { j }F(x,y,z)=−6x2i+12y3j​

Suppose $\vec { F } ( x , y , z ) = - 6 x ^ { 2 } \vec { i } + 12 y ^ { 3 } \vec { j }$