(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [itex]\phi[/itex](x,y,z) = x^{3}+ 2xy +yz^{3}find [itex]\nabla[/itex][itex]\phi[/itex] at the point P=(1,1,2) and direction of the unit normal to the surface [itex]\phi[/itex](x,y,z) = 11 at P.

2. Relevant equations

3. The attempt at a solution

Worked out [itex]\nabla[/itex][itex]\phi[/itex] to be 5i + 10j + 12k

Got |[itex]\nabla[/itex][itex]\phi[/itex]|= √256

so the unit normal to surface is surely [itex]\frac{5+10+12}{√269}[/itex]

but how does the =11 bit make a difference?

Thanksss

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# Homework Help: Vector Calculus, Unit normal to surface help

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