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10. LO 6 & 7: Draw the resultant vector for the following: 17+R

10. LO 6 & 7: Draw the resultant vector for the following: 17+R

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Title: Understanding Resultant Vectors ### Vector Addition Practice **Objective:** Learn how to draw the resultant vector for given vector pairs. ### Given Vector Operations: 1. \( \vec{A} + \vec{B} \) 2. \( \vec{B} + \vec{A} \) 3. \( \vec{A} - \vec{B} \) 4. \( \vec{B} - \vec{A} \) 5. \( 2\vec{A} - \vec{B} \) ### Diagram Explanation: - Two vectors are represented by arrows: - **Vector A**: Shown as an arrow pointing slightly downward. - **Vector B**: Shown as an arrow pointing almost directly upward. ### Rules for Adding Vectors: - **Rule 1:** Add vectors head (arrow tip) to tail (origin of the arrow). - **Rule 2:** The resultant vector goes from the tail of the first vector to the head of the last. *(Place a marker at the tail of the first vector for clarity.)* - **Rule 3:** The order of adding vectors doesn’t matter, but maintaining correct direction is crucial—ensure to use proper reference degrees. - **Rule 4:** A negative sign with a vector indicates it moves in the opposite direction. *(Think of this as algebraic addition.)* - **Rule 5:** On a Cartesian Coordinate System, draw the angle of the resultant by rotating counterclockwise from the positive x-axis (0 degrees) to the resultant direction. Assume: - \( +x = 0 \) degrees - \( +y = 90 \) degrees - \( -x = 180 \) degrees - \( -y = 270 \) degrees, unless stated otherwise. ### Conclusion Understanding how to determine and draw resultant vectors using these rules is fundamental in vector mathematics and physics, simplifying complex vector interactions into visually comprehensible forms.
Transcribed Image Text:Title: Understanding Resultant Vectors ### Vector Addition Practice **Objective:** Learn how to draw the resultant vector for given vector pairs. ### Given Vector Operations: 1. \( \vec{A} + \vec{B} \) 2. \( \vec{B} + \vec{A} \) 3. \( \vec{A} - \vec{B} \) 4. \( \vec{B} - \vec{A} \) 5. \( 2\vec{A} - \vec{B} \) ### Diagram Explanation: - Two vectors are represented by arrows: - **Vector A**: Shown as an arrow pointing slightly downward. - **Vector B**: Shown as an arrow pointing almost directly upward. ### Rules for Adding Vectors: - **Rule 1:** Add vectors head (arrow tip) to tail (origin of the arrow). - **Rule 2:** The resultant vector goes from the tail of the first vector to the head of the last. *(Place a marker at the tail of the first vector for clarity.)* - **Rule 3:** The order of adding vectors doesn’t matter, but maintaining correct direction is crucial—ensure to use proper reference degrees. - **Rule 4:** A negative sign with a vector indicates it moves in the opposite direction. *(Think of this as algebraic addition.)* - **Rule 5:** On a Cartesian Coordinate System, draw the angle of the resultant by rotating counterclockwise from the positive x-axis (0 degrees) to the resultant direction. Assume: - \( +x = 0 \) degrees - \( +y = 90 \) degrees - \( -x = 180 \) degrees - \( -y = 270 \) degrees, unless stated otherwise. ### Conclusion Understanding how to determine and draw resultant vectors using these rules is fundamental in vector mathematics and physics, simplifying complex vector interactions into visually comprehensible forms.
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