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

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Two nonzero perpendicular vectors cannot be added together to equal zero. The discussion highlights that while one might think of vectors canceling each other out, this only occurs if they are aligned in opposite directions with equal magnitudes. Perpendicular vectors, such as (0,1) and (1,0), maintain a fixed angle of 90 degrees, preventing their sum from being zero. The concept of orthogonality implies that the vectors do not influence each other's direction in a way that would allow for cancellation. Ultimately, the geometry of perpendicular vectors reinforces that their resultant cannot be zero.
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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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