I am learning Calc III and am up to the section about gradients and directional derivatives. I was given a word problem involving a person on a mountain who measures a 4-degree rise due west and a 3-degree rise due north. I know that when facing east the slope of a terrain is given by \(\frac{\partial f}{\partial }\) and when facing north the slope of a terrain is given by \(\frac{\partial f}{\partial y}\) but what is the slope when facing west? Is it \(\frac{\partial f}{\partial z}\)?
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Word problems for gradients and directional derivatives
- Thread starter burt
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Deleted member 4993
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As I see it:I am learning Calc III and am up to the section about gradients and directional derivatives. I was given a word problem involving a person on a mountain who measures a 4-degree rise due west and a 3-degree rise due north. I know that when facing east the slope of a terrain is given by \(\frac{\partial f}{\partial }\) and when facing north the slope of a terrain is given by \(\frac{\partial f}{\partial y}\) but what is the slope when facing west? Is it \(\frac{\partial f}{\partial z}\)?
slopes facing east or west does not change "mathematically", in magnitude. Of course, while facing west - what was "elevation", will become "depression" while facing east.
What do you mean by that?As I see it:
slopes facing east or west does not change "mathematically", in magnitude. Of course, while facing west - what was "elevation", will become "depression" while facing east.
So I can treat it in the same wayslopes facing east or west does not change "mathematically", in magnitude.
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Deleted member 4993
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with same magnitude (number) - not direction.So I can treat it in the same way
How can I deal with the direction change?with same magnitude (number) - not direction.
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Deleted member 4993
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You need to think about it!!How can I deal with the direction change?
Which way is your x-axis? Which way is its unit vector?
Which way is your y-axis? Which way is its unit vector?
I
If I face west instead of east, that means I'm facing the negative x axis instead of the positive ones. So, my magnitude is correct, I just need to flip the direction?You need to think about it!!
Which way is your x-axis? Which way is its unit vector?
Which way is your y-axis? Which way is its unit vector?