---
title: "Vectors \\( \\vec{A} \\) and \\( \\vec{B} \\) originate from the same point on a set of perpendicular \\( x \\)– and \\( y \\)-axes as shown in the accompanying figure. Vector \\( \\vec{A} \\) has magnitude \\( 6.3 \\) and is directed \\( 23^{\\circ} \\) to the left of the positive \\( y \\)-axis. Vector \\( \\vec{B} \\) has magnitude \\( 5.7 \\) and is directed \\( 34^{\\circ} \\) above the positive \\( x \\)-axis. A third vector is defined by \\( \\vec{C} = \\vec{B} – \\vec{A} \\). What is the magnitude of \\( \\vec{C} \\)?"
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url: "https://nerd-notes.com/ubq/114139/"
date_modified: "2026-08-18T02:37:55+00:00"
---

# Vectors \( \vec{A} \) and \( \vec{B} \) originate from the same point on a set of perpendicular \( x \)– and \( y \)-axes as shown in the accompanying figure. Vector \( \vec{A} \) has magnitude \( 6.3 \) and is directed \( 23^{\circ} \) to the left of the positive \( y \)-axis. Vector \( \vec{B} \) has magnitude \( 5.7 \) and is directed \( 34^{\circ} \) above the positive \( x \)-axis. A third vector is defined by \( \vec{C} = \vec{B} – \vec{A} \). What is the magnitude of \( \vec{C} \)?

Vectors \( \vec{A} \) and \( \vec{B} \) originate from the same point on a set of perpendicular \( x \)– and \( y \)-axes as shown in the accompanying figure. Vector \( \vec{A} \) has magnitude \( 6.3 \) and is directed \( 23^{\circ} \) to the left of the positive \( y \)-axis. Vector \( \vec{B} \) has magnitude \( 5.7 \) and is directed \( 34^{\circ} \) above the positive \( x \)-axis. A third vector is defined by \( \vec{C} = \vec{B} – \vec{A} \). What is the magnitude of \( \vec{C} \)?

![A two-dimensional Cartesian coordinate system with the origin at the center. The positive ( x )-axis extends horizontally to the right and is labeled “x” at its arrowhead. The positive ( y )-axis extends vertically upward and is labeled “y” at its arrowhead. A thin line continues the axes past the origin into the negative directions, with arrowheads at both negative ends. nnTwo bold vectors originate from the origin. n1. Vector ( vec{A} ) is drawn into the second quadrant, making an angle of ( 23^{circ} ) to the left of the positive ( y )-axis (equivalently ( 67^{circ} ) above the negative ( x )-axis). Its arrowhead points up-left. Near the arrow is the bold letter “A”; beside the vector, the magnitude “6.3” is printed. An arc between the vector and the positive ( y )-axis is marked with the label “23°.” n2. Vector ( vec{B} ) is drawn into the first quadrant, making an angle of ( 34^{circ} ) above the positive ( x )-axis. Its arrowhead points up-right. Near the arrow is the bold letter “B”; beside the vector, the magnitude “5.7” is printed. An arc between the vector and the positive ( x )-axis is marked with the label “34°.” nnNo other vectors are drawn. All vectors originate exactly at the origin and are drawn to scale relative to one another and to the printed magnitudes.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-114139-1782701429-LMubEQ.jpg)

- **A.** \[ 3.9 \]
- **B.** \[ 5.9 \]
- **C.** \[ 6.8 \]
- **D.** \[ 7.7 \]
- **E.** \[ 8.4 \]

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114139/*