Optimal Direction for Mosquito Flight to Warmth

[abrowaqas]

Homework Statement

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?

Homework Equations

Grad T = Txi+Tyj+Tkz

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

 

[lanedance]

looks ok to me

 

[Mark44]

Homework Statement

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?

Homework Equations

Grad T = Txi+Tyj+Tkz

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

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?

 

[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.

 

[lanedance]

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