How Do You Add Vectors Using Unit Vector Notation?

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Homework Help Overview

The discussion revolves around the addition of vectors using unit vector notation, specifically focusing on two given vectors, a and b, and the subsequent calculations of their sum, magnitude, and direction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand the notation of unit vectors and how to add them, expressing uncertainty about the graphical method they are familiar with. They also raise questions about the correctness of their calculated angle for the resultant vector.

Discussion Status

Some participants have provided clarifications regarding the meaning of unit vectors and the conventions for reporting angles. The discussion is exploring different interpretations of the angle measurement and the conventions used in vector addition.

Contextual Notes

Participants are considering the conventions for reporting angles in vector addition, specifically whether to measure counterclockwise from the positive x-axis. There is also a mention of the original poster's confusion regarding the direction of the resultant vector.

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Homework Statement



Consider the following vectors:

a = (5.0m) i + (2.0m) j
b = (-14m) i + (6.0m)j

Sum of a+b in unit vector notation?

Homework Equations





The Attempt at a Solution



I'm not sure about this notation, all I know about adding vectors is graphically. Does (5.0m) i + (2.0m) j mean 5 meters in direction i and 2 in direction j?
 
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Yes, conventionally, i, j, and k are dimensionless unit vectors pointing, respectively, in the +x, +y and +z directions.
 
Alright, got it.

Now I am asked for magnitude and direction of new vector. After adding these, I found magnitude to be 12.04 which is correct, but direction is stumping me.

I used trig to get the angle 41.64 as the angle direction of the new vector, but I'm not sure I'm finding the correct angle. After placing the vectors head to tail, I found the angle between the hypotenuse and x-axis. Is this the wrong angle?

Since it's pointing upwards and to the left, should I add 90* to my angle?
 
What convention are you going to use to report the angle of the resultant? A common convention is CCW from the +x axis.
 

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