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3. Let x, y be any two vectors. Assume that ||x+y|| = |x|| = ||y|| Find the angle between x, y. (Hint: Begin by squaring both sides of the first equation given above. Alternatively, use geometry as a guide. Your proof cannot rely on geometry, but it is a strong starting point.)

3. Let x, y be any two vectors. Assume that ||x+y|| = |x|| = ||y|| Find the angle between x, y. (Hint: Begin by squaring both sides of the first equation given above. Alternatively, use geometry as a guide. Your proof cannot rely on geometry, but it is a strong starting point.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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3. Let x, y be any two vectors. Assume that ||x + y|| = ||x|| = ||y|| Find the angle between x, y. (Hint: Begin by squaring both sides of the first equation given above. Alternatively, use geometry as a guide. Your proof cannot rely on geometry, but it is a strong starting point.) 4. Use the 3-space standard basis vectors to find three nonzero vectors a, b, c satisfying axb = a x c, where a × b 0 and b c. (This proves that the cross product operation does not have cancellation across equations.)
Transcribed Image Text:3. Let x, y be any two vectors. Assume that ||x + y|| = ||x|| = ||y|| Find the angle between x, y. (Hint: Begin by squaring both sides of the first equation given above. Alternatively, use geometry as a guide. Your proof cannot rely on geometry, but it is a strong starting point.) 4. Use the 3-space standard basis vectors to find three nonzero vectors a, b, c satisfying axb = a x c, where a × b 0 and b c. (This proves that the cross product operation does not have cancellation across equations.)
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