Pythagorean triplet and vectors

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SUMMARY

The discussion centers on the relationship between vectors A, B, and C, specifically examining the equations A - B = C and C = A + B. The Pythagorean triplet 3, 4, 5 is referenced to illustrate the first equation, confirming that A - B can equal C under certain conditions. The second equation, C = A + B, is also possible when considering vectors in opposite directions, demonstrating the versatility of vector addition and subtraction in geometric contexts.

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  • Understanding of vector operations, including addition and subtraction
  • Familiarity with the Pythagorean theorem and triplets
  • Basic knowledge of geometric representations of vectors
  • Concept of vector direction and magnitude
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  • Study vector addition and subtraction in detail using graphical representations
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Students of mathematics and physics, educators teaching vector concepts, and anyone interested in the geometric interpretation of vectors and their relationships.

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Suppose that vectors A, B and C are related by A-B=C.

a) Is it possible that A-B=C? If so, draw the sort of situation when this is so. (A is the magnitude of A, B of B and C of C.)

b) Is it possible that C=A+B? If so, then draw the sort of situation when this is so.

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a) I used the Pythagorean triplet 3,4,5 for this situation.
b) I'm not sure but I think the question basically asks whether C can equal A+B and at the same time can C equal the square root of the sum of the squares of A and B. I'm having trouble getting my head around this.
 
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OK never mind, false alarm. For some reason I was thinking strictly in the form of triangles for my vector subtraction. I believe situation b) is possible if you have any two vectors of opposite direction.
 

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