Question

The temperature at the point (x, y, z) in space is given by T ( x, y, z) = x + yz. A fly is at the point (1, 2, 1). In what direction should he begin to fly to cool off as quickly as possible. Your answer should be a unit vector in the requested direction.

Answer 1

Answer:

$u= -\frac{1}{\sqrt{6}} ,-\frac{1}{\sqrt{6}} ,-\frac{2}{\sqrt{6}}$

Step-by-step explanation:

From the question we are told that

Temperature is given $T ( x, y, z) = x + yz.$\

A fly is at (1,2,1)

Generally the direction of fly is given by

     

      $\triangleT(x,y,z) =(1,z,y)$

       $v= \triangleT(1,2,1)\\v=(1,1,2)$

Mathematically solving for the vector direction

       $|v|=\sqrt{1^2+1^2+2^2}$

       $|v|=\sqrt{6}$

       $u=- \frac{v}{|v|}$

       $u= -\frac{1}{\sqrt{6}} ,-\frac{1}{\sqrt{6}} ,-\frac{2}{\sqrt{6}}$

Therefore this the direction which should be taken to cool down soonest