Vector Calculus, Unit normal to surface help

[tarwe]

Homework Statement

If \phi(x,y,z) = x³ + 2xy +yz³ find \nabla\phi at the point P=(1,1,2) and direction of the unit normal to the surface \phi(x,y,z) = 11 at P.

Homework Equations

The Attempt at a Solution

Worked out \nabla\phi to be 5i + 10j + 12k
Got |\nabla\phi|= √256

so the unit normal to surface is surely \frac{5+10+12}{√269}
but how does the =11 bit make a difference?

Thanksss

 

[tiny-tim]

welcome to pf!

hi tarwe! welcome to pf!

but how does the =11 bit make a difference?

it doesn't

(btw, it's not 256)

 

[tarwe]

hi tarwe! welcome to pf!


it doesn't

(btw, it's not 256)

thank you!
that was a typo, meant 269, was thinking in binary :/

 

[HallsofIvy]

Homework Statement

If \phi(x,y,z) = x³ + 2xy +yz³ find \nabla\phi at the point P=(1,1,2) and direction of the unit normal to the surface \phi(x,y,z) = 11 at P.

Homework Equations

The Attempt at a Solution

Worked out \nabla\phi to be 5i + 10j + 12k
Got |\nabla\phi|= √256

so the unit n0ormal to surface is surely \frac{5+10+12}{√269}

You mean \frac{5i+10j+12k}{√269}

but how does the =11 bit make a difference?

It would change the exact position but not the normal to the surface.

Thanksss

Homework Statement

Homework Equations

The Attempt at a Solution