Find Magnitude & Direction of A+B - Unit Vector Help

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Homework Help Overview

The discussion revolves around finding the magnitude and direction of the vector sum A + B, where A and B are given in rectangular coordinates. The vectors are A = -4 i - 1 j and B = 8 i - 2 j.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss how to add the components of the vectors to find the resultant in rectangular coordinates. There are questions about converting the resultant vector from rectangular to polar coordinates to determine magnitude and direction.

Discussion Status

Some participants have provided guidance on the conversion process from rectangular to polar coordinates and have clarified the distinction between rectangular and polar representations of vectors. There is an ongoing exploration of how to express the resultant vector and its angle.

Contextual Notes

There is mention of specific requirements from a web-based homework platform regarding the format of the answer, indicating that a single numerical value is expected, which may refer to the angle or magnitude.

Loppyfoot
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Homework Statement


Find the magnitude and direction of A + B for the following vectors.

A = -4 i - 1 j, B = 8 i -2 j

How do I find the magnitude of A+B, and also the degree clockwise from the +x direction?
 
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Loppyfoot said:

Homework Statement


Find the magnitude and direction of A + B for the following vectors.

A = -4 i - 1 j, B = 8 i -2 j

How do I find the magnitude of A+B, and also the degree clockwise from the +x direction?

You add the components to get the resultant, which is also in rectangular coordinates. Do you know how to convert the resultant vector from rectangular coordinates to polar coordinates (so you can get the resultant magnitude and direction)?
 
So would it be 4i - 3j? On my webassign homework, it has to be a single numerical value.
 
Loppyfoot said:
So would it be 4i - 3j? On my webassign homework, it has to be a single numerical value.

That's the correct answer in rectangular coordinates. If they are asking for a single number for an answer, did you say they want the angle that the vector forms with some axis? A vector is always made up of 2 numbers (in 2 dimensions). In rectangular coordinates, it's the i and j components. In polar coordinates, it's the magnitude and direction (usually the direction is the angle swinging up from the x-axis to the vector).

Do you know how to convert the vector from rectangular to polar coordinates? That should be in your book.
 
Got it. Thanks man!
 

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