Physics Help Forum Dot Product Help

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 Oct 7th 2017, 06:07 PM #1 Junior Member   Join Date: Oct 2017 Posts: 11 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.
Oct 8th 2017, 06:58 AM   #2
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Join Date: Aug 2010
Posts: 240
 Originally Posted by alex34 " 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"?

 Oct 8th 2017, 09:08 AM #3 Junior Member   Join Date: Oct 2017 Posts: 11 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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