Pythagorean Theorem proof Vector Calc. Due tomorrow 9am. PLEASE HELP

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SUMMARY

The discussion centers on proving the Pythagorean theorem using vector calculus. Specifically, it states that for vectors a, b, and c in Rn, if a + b = c and the dot product a.b = 0, then the equation ||a||² + ||b||² = ||c||² holds true. The condition a.b = 0 indicates that vectors a and b are orthogonal, forming a right triangle, which is essential for applying the theorem. The hint provided emphasizes the geometric interpretation of the vectors as forming a right triangle.

PREREQUISITES
  • Understanding of vector operations in Rn
  • Knowledge of the dot product and its implications
  • Familiarity with the concept of vector norms
  • Basic principles of trigonometry, particularly the cosine rule
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  • Study the properties of orthogonal vectors in vector spaces
  • Learn about vector norms and their geometric interpretations
  • Explore the cosine rule and its applications in triangle geometry
  • Investigate proofs of the Pythagorean theorem in different mathematical contexts
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Students studying vector calculus, mathematics educators, and anyone seeking to understand the geometric foundations of the Pythagorean theorem.

rgalvan2
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Pythagorean Theorem proof Vector Calc. Due tomorrow 9am. PLEASE HELP!

Prove the Pythagorean theorem. That is, if a,b, and c are vectors in Rn such that a + b = c and a.b = 0, then ||a||2 + ||b||2 = ||c||2. Why is this called the Pythagorean theorem.

Hint given: Given the hypotheses, you have a right triangle. Why?

Help please! This is due tomorrow morning and I cannot figure it out.

||x||= length of variable
a.b= dot product
 
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rgalvan2 said:
Hint given: Given the hypotheses, you have a right triangle. Why?

Well what does [tex]a \cdot b = 0[/tex] tell you about the vectors a and b?
 


Draw a triangle,explain why the angle is 90 degrees and then think cosine rule.
 

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