Question

Can anyone help me with where I went wrong?

Answer 1

First I needed the unit vector of Q since the norm is not 1.

So my unit vector was:

= < 2/√(2²+4²+5²) , 4/√(2²+4²+5²) , 5/√(2²+4²+5²) >

= < 2/√(45) , 4/√(45) , 5/√(45) >

Next, I needed the directional derivative of f(x,y,z)

So I got that ∇f=< y+z , x+z , y+z >

So therefore, ∇f(3,-3,3) = <0,6,0>

So if we take the dot product with the unit vector I get:

∇f(3,-3,3) * < 2/√(45) , 4/√(45) , 5/√(45) >

<0,6,0> * < 2/√(45) , 4/√(45) , 5/√(45) >

This simplifies down to:

0+24/√(45)+0

24/√(45) which is my answer.

Answer 2

I honestly don't see where I went wrong...

Answer 3

Your answer is right, but sometimes online homework is picky about the answer it accepts. Try rationalizing the denominator.

Answer 4

my textbook for differential equations is like that too...super picky like crazy

Answer 5

Link to wolfram for the interested: http://www.wolframalpha.com/input/?i=derivative+of+f%28x%2Cy%2Cz%29%3Dxy%2Bxz%2Byz+in+direction+of+%282%2C4%2C5%29+when+x%3D3%2Cy%3D-3%2Cz%3D3

Answer 6

Ohh I know what I did wrong!!! @SithsAndGiggles

Answer 7

I forgot to find the distancce from P and Q XD .

Answer 8

Ah, I forgot about the details of the directional derivative. I just followed your work :/

Answer 9

Haha. Thanks though :) .