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Chapter 1. Vectors and Matrices 9. With regard to the proof of Proposition 2.3, how is toy related to x ? What proj,x? 10. Use vector methods to prove that a parallelogram is a rectangle if and only the same length. 11. Use the fundamental properties of the dot product to prove that x + ylP+ x - yll2 2 (lxl2 1ly2) Interpret the result geometrically. *12. Use the dot product to prove the law of cosines: As shown in Figure 2.4, c2= a2 b2- 2ab cos 0. B C a A b Figure 2.4 13. Use vector methods to prove that the diagonals of a parallelogram are ort the parallelogram is a rhombus (i.e., has all sides of equal length). 14. Use vector methods to prove that a triangle inscribed in a circle and havin its sides must be a right triangle. (Hint: See Figure 2.5.) Geometric challenge: More generally, given two points A and B in the of points X so that ZAXB has a fixed measure?

Chapter 1. Vectors and Matrices 9. With regard to the proof of Proposition 2.3, how is toy related to x ? What proj,x? 10. Use vector methods to prove that a parallelogram is a rectangle if and only the same length. 11. Use the fundamental properties of the dot product to prove that x + ylP+ x - yll2 2 (lxl2 1ly2) Interpret the result geometrically. *12. Use the dot product to prove the law of cosines: As shown in Figure 2.4, c2= a2 b2- 2ab cos 0. B C a A b Figure 2.4 13. Use vector methods to prove that the diagonals of a parallelogram are ort the parallelogram is a rhombus (i.e., has all sides of equal length). 14. Use vector methods to prove that a triangle inscribed in a circle and havin its sides must be a right triangle. (Hint: See Figure 2.5.) Geometric challenge: More generally, given two points A and B in the of points X so that ZAXB has a fixed measure?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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For problem 11, I have done the proof, but don't know how to interpret the result geometrically. Please help me! Thank you very much!

Chapter 1. Vectors and Matrices 9. With regard to the proof of Proposition 2.3, how is toy related to x ? What proj,x? 10. Use vector methods to prove that a parallelogram is a rectangle if and only the same length. 11. Use the fundamental properties of the dot product to prove that x + ylP+ x - yll2 2 (lxl2 1ly2) Interpret the result geometrically. *12. Use the dot product to prove the law of cosines: As shown in Figure 2.4, c2= a2 b2- 2ab cos 0. B C a A b Figure 2.4 13. Use vector methods to prove that the diagonals of a parallelogram are ort the parallelogram is a rhombus (i.e., has all sides of equal length). 14. Use vector methods to prove that a triangle inscribed in a circle and havin its sides must be a right triangle. (Hint: See Figure 2.5.) Geometric challenge: More generally, given two points A and B in the of points X so that ZAXB has a fixed measure?
Transcribed Image Text:Chapter 1. Vectors and Matrices 9. With regard to the proof of Proposition 2.3, how is toy related to x ? What proj,x? 10. Use vector methods to prove that a parallelogram is a rectangle if and only the same length. 11. Use the fundamental properties of the dot product to prove that x + ylP+ x - yll2 2 (lxl2 1ly2) Interpret the result geometrically. *12. Use the dot product to prove the law of cosines: As shown in Figure 2.4, c2= a2 b2- 2ab cos 0. B C a A b Figure 2.4 13. Use vector methods to prove that the diagonals of a parallelogram are ort the parallelogram is a rhombus (i.e., has all sides of equal length). 14. Use vector methods to prove that a triangle inscribed in a circle and havin its sides must be a right triangle. (Hint: See Figure 2.5.) Geometric challenge: More generally, given two points A and B in the of points X so that ZAXB has a fixed measure?
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