Can Nonzero Perpendicular Vectors Be Added to Equal Zero? | Quick Question

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Homework Help Overview

The discussion revolves around the question of whether two nonzero perpendicular vectors can be added together to yield a sum of zero. The subject area is vector mathematics, particularly focusing on the properties of perpendicular (orthogonal) vectors.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about the possibility of two nonzero perpendicular vectors summing to zero. Participants inquire about the reasoning behind this inclination and suggest exploring definitions and properties of orthogonal vectors. Some participants propose considering the magnitudes and directions of the vectors involved.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the properties of perpendicular vectors. Guidance has been offered regarding the implications of orthogonality and suggestions to visualize the problem through drawings and equations.

Contextual Notes

One participant notes a lack of familiarity with orthonormal bases, which may be influencing their understanding of the problem. There is an emphasis on the need to clarify definitions and properties related to perpendicular vectors.

Cursed
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Can two nonzero perpendicular vectors be added together so their sum is zero?

I want to say yes, but I'm not sure. :rolleyes:
 
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Thread moved to Homework Help. What are your thoughts, Cursed? Why are you inclined to say yes, and how do you think you could go about proving it? Have you studied orthonormal bases yet? What does the term perpendicular (or orthogonal) imply?
 
berkeman said:
Thread moved to Homework Help. What are your thoughts, Cursed? Why are you inclined to say yes, and how do you think you could go about proving it? Have you studied orthonormal bases yet? What does the term perpendicular (or orthogonal) imply?

No, I haven't studied orthonormal bases yet. That's probably why I don't understand it. :-p

I figured that one vector could cancel out the other provided that both their magnitudes are equivalent, and if one vector component is negative while the other one is positive.
 
Think about what the term perpendicular (orthogonal) means. One set of perpendicular vectors would be (0,1) and (1,0), for example. Or the two vectors could be rotated together to any angle in the x-y plane, but still in the perpendicular position. Write some equations that would define two orthogonal vectors...do you see anything special?
 
Have you considered drawing a picture? Draw two perpendicular vectors. There sum can be found using the "parallelogram law" which, in the case of perpendicular vectors is a "rectangle". Can you find a rectangle, with non-zero sides that has a diagonal of length 0?
 

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