Find the magnitude and direction of each vector

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Homework Help Overview

The discussion revolves around vector analysis, specifically focusing on three given vectors A, B, and C. Participants are tasked with finding the magnitude and direction of each vector, as well as exploring resultant vectors and a vector equation involving coefficients.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the interpretation of finding the direction of vectors, questioning whether it refers to the angle relative to the positive x-axis. There is mention of adding vector components for resultant calculations and the nature of the vector equation in part C, noting it leads to two equations from one vector equation.

Discussion Status

The discussion is active, with participants confirming interpretations and exploring the implications of the vector equation. Some guidance has been provided regarding the approach to solving the equations derived from the vector equation.

Contextual Notes

Participants are navigating the requirements of the homework, including the need to find both magnitude and direction, as well as the implications of the vector equation involving two unknowns.

joemama69
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Homework Statement


2. You are given three vectors: A = (6.0i— 8.0j) units B = (-8.0i + 3.0j) units and C = (26.0i + 19.0j) units.

a) Find the magnitude and direction of each vector.


b) Find the resultant of A + B, A - B and A + B - C.

c) It is know that aA + bB + C = 0. Find the values of a and b that satisfy this vector equation.


Homework Equations





The Attempt at a Solution



For part A, what does it mean to find the direction of each vector. do they want the angle
 
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joemama69 said:

Homework Statement


2. You are given three vectors: A = (6.0i— 8.0j) units B = (-8.0i + 3.0j) units and C = (26.0i + 19.0j) units.

a) Find the magnitude and direction of each vector.


b) Find the resultant of A + B, A - B and A + B - C.

c) It is know that aA + bB + C = 0. Find the values of a and b that satisfy this vector equation.


Homework Equations





The Attempt at a Solution



For part A, what does it mean to find the direction of each vector. do they want the angle

yes they do
 


I assume they want the angle of the vector. By convention, the angle is measured counter-clockwise from the positive x axis. Think of how you drew the unit circle in trigonometry.

For B, you simply add components.

Part C, you Have what appears to be one equation and two unknowns. However, it's a vector equation, which in your case is actually two equations. There's one for your x components and one for your y components.
 


so i would do

a(6.0i— 8.0j) +b(-8.0i + 3.0j) + (26.0i + 19.0j) = 0

6a - 8b + 26 = 0

-8a + 3b + 19 = 0 and just solve this system
 


Yes. Correct
 

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