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

`u= -(1)/(√(6)) ,-(1)/(√(6)) ,-(2)/(√(6))`

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|=√(1^2+1^2+2^2)`

`|v|=√(6)`

`u=- (v)/(|v|)`

`u= -(1)/(√(6)) ,-(1)/(√(6)) ,-(2)/(√(6))`

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