# Vector analysis problem

1. Aug 12, 2010

### abrowaqas

1. The problem statement, all variables and given/known data
The temperature at a point (x,y,z) in space is given by
T(x,y,z) = x^2+y^2-z. a mosquito located at (1,1,2) desires to fly in such a direction that it will get warm as soon as possible. in what direction should it fly?

2. Relevant equations

3. The attempt at a solution
i first take its grad T = 2xi+2yj-k

then for direction i just get its unit vector.... that is 1/3(2xi+2yj-k) ..

am i right or wrong

2. Aug 16, 2010

### lanedance

looks ok to me

3. Aug 16, 2010

### Staff: Mentor

You didn't use the information that the mosquito starts at (1, 1, 2). Also, why do you think that (1/3)(2xi + 2yj - k) is a unit vector?

4. Aug 17, 2010

### HallsofIvy

How did a problem involving the gradient of a vector function get into the "Precalculus Homework" section? I'm going to move this to the "Calculus and beyond" section.

(1/3)(2i+ 2j- k) is a unit vector. Whether or not (1/3)(2xi+ 2yj- k) is depends upon the values of x and y.

5. Aug 17, 2010

### lanedance

sorry, looked a little quickly & got the jist of it - all good pick-ups