(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A scalar field is given by the function: ∅ = 3x^{2}y + 4y^{2}

a) Find del ∅ at the point (3,5)

b) Find the component of del ∅ that makes a -60^{o}angle with the axis at the point (3,5)

2. Relevant equations

del ∅ = d∅/dx + d∅/dy

3. The attempt at a solution

I completed part a:

del ∅ = (6xy+4y^{2})[itex]\hat{i}[/itex] + (3x^{2}+8y)[itex]\hat{j}[/itex] = 120[itex]\hat{i}[/itex] + 67[itex]\hat{j}[/itex] (this answer is correct)

I am having trouble with part b. My gut feeling is that I need to take a dot product; project the vector from 'part a' onto the vector that makes "a -60^{o}angle with the axis."

Assuming the equation is |a||b|cosθ,

- I think a = 120[itex]\hat{i}[/itex] + 67[itex]\hat{j}[/itex]
- I'm not sure what b is. Maybe a unit vector?
- I'm thinking θ is 60
^{o}+ atan(67/120)

Also, I'm assuming the "axis" that the problem refers to is the x-axis. The answer is -13.02.

Thank you for any help.

EDIT: Oops. 120i + 67j is not correct; it's 90i + 67j. |90i + 67j|cos(60+atan(67/90)) = -13.02

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# Partial Derivative: Finding the vector on a scalar field at point (3,5)

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