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geniusboy [140]
3 years ago
5

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 dire

ction should he begin to fly to cool off as quickly as possible. Your answer should be a unit vector in the requested direction.
Mathematics
1 answer:
kow [346]3 years ago
7 0

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

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