---
title: "A particle is constrained to move in the xy-plane under the influence of a conservative force. The potential energy of the particle as a function of position is given by \\(U(x,y) = C(x^2 + 2y^2)\\), where \\(C\\) is a positive constant. Which of the following vector diagrams best represents the direction and relative components of the net force \\(\\vec{F}\\) exerted on the particle when it is at position \\((x,y) = (d, d)\\), where \\(d > 0\\)?"
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url: "https://nerd-notes.com/ubq/120719/"
date_modified: "2026-08-23T04:42:50+00:00"
---

# A particle is constrained to move in the xy-plane under the influence of a conservative force. The potential energy of the particle as a function of position is given by \(U(x,y) = C(x^2 + 2y^2)\), where \(C\) is a positive constant. Which of the following vector diagrams best represents the direction and relative components of the net force \(\vec{F}\) exerted on the particle when it is at position \((x,y) = (d, d)\), where \(d > 0\)?

A particle is constrained to move in the xy-plane under the influence of a conservative force. The potential energy of the particle as a function of position is given by \(U(x,y) = C(x^2 + 2y^2)\), where \(C\) is a positive constant. Which of the following vector diagrams best represents the direction and relative components of the net force \(\vec{F}\) exerted on the particle when it is at position \((x,y) = (d, d)\), where \(d > 0\)?

![A two-dimensional Cartesian coordinate plane showing a horizontal x-axis and a vertical y-axis intersecting at an origin labeled O. In the first quadrant, a single point labeled P is plotted. A horizontal dashed line connects point P to the y-axis at a tick mark labeled d. A vertical dashed line connects point P to the x-axis at a tick mark labeled d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460168-V5t0PA.jpg)

- **A.** A vector originating at \((d,d)\) pointing in the \(+x\) and \(+y\) directions with \(F_y = 2F_x\)
- **B.** A vector originating at \((d,d)\) pointing in the \(-x\) and \(-y\) directions with \(|F_x| = 2|F_y|\)
- **C.** A vector originating at \((d,d)\) pointing in the \(-x\) and \(-y\) directions with \(|F_y| = 2|F_x|\)
- **D.** A vector originating at \((d,d)\) pointing in the \(-x\) and \(-y\) directions with \(|F_x| = |F_y|\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120719/*