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Old Oct 7th 2017, 05:07 PM   #1
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Question Dot Product Help

" What force vector corresponds to a potential energy U=-3x^2+5xy+z^-2 ?"
By taking the derivative with respect to xyz in each I end with F = (6x+5y)i + (-5x)j + (2z)k
Then I am asked to determine the power if the velocity it moves with is v = (x+2y-z)j
I know power = FdotV

so.. (6x+5y)i multiplied by 0 = 0
(-5x)j multipled by (x+2y-z)j = -5 + 0 + 0 = -5 <-- This is what i am unsure about. Dotting two vectors with multiple variables. Please let me know if I did or didnt do it correctly. Thank you.
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Old Oct 8th 2017, 05:58 AM   #2
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Originally Posted by alex34 View Post
" What force vector corresponds to a potential energy U=-3x^2+5xy+z^-2 ?"
By taking the derivative with respect to xyz in each I end with F = (6x+5y)i + (-5x)j + (2z)k
Yes, the force corresponding to a given potential energy is its "gradient".

Then I am asked to determine the power if the velocity it moves with is v = (x+2y-z)j
I know power = FdotV

so.. (6x+5y)i multiplied by 0 = 0
(-5x)j multipled by (x+2y-z)j = -5 + 0 + 0 = -5 <-- This is what i am unsure about. Dotting two vectors with multiple variables. Please let me know if I did or didnt do it correctly. Thank you.
Yes, with v having 0 x and z components, the dot product of F with v is ((-5x)(x+ 2y- z)= 5x^2+ 10xy- 5xz. That depends on the values of x, y, and z. Where did you get "-5+ 0+ 0"?
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Old Oct 8th 2017, 08:08 AM   #3
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I was not sure if I was "allowed" to multiple the -5x with the y and z. I thought the -5x could only be multiplied with x's and y's with other y variables etc. Thank you !
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