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(1) Let a and b denote two vectors. Try to prove (a x b)² = a²b² – (a · b)² (2) For the triangle ABC, let a, b and c denote the length of BC, AC and AB. Based on the above theory, try to prove that the area of the triangle ABC equals to VP(p – a)(p – b)(p – c) where p= (a+b+c)/2 B

(1) Let a and b denote two vectors. Try to prove (a x b)² = a²b² – (a · b)² (2) For the triangle ABC, let a, b and c denote the length of BC, AC and AB. Based on the above theory, try to prove that the area of the triangle ABC equals to VP(p – a)(p – b)(p – c) where p= (a+b+c)/2 B

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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(1) Let a and b denote two vectors. Try to prove (a x b)² = a²b² – (a · b)² (2) For the triangle ABC, let a, b and c denote the length of BC, AC and AB. Based on the above theory, try to prove that the area of the triangle ABC equals to VP(p – a)(p – b)(p – c) where p= (a+b+c)/2 B
Transcribed Image Text:(1) Let a and b denote two vectors. Try to prove (a x b)² = a²b² – (a · b)² (2) For the triangle ABC, let a, b and c denote the length of BC, AC and AB. Based on the above theory, try to prove that the area of the triangle ABC equals to VP(p – a)(p – b)(p – c) where p= (a+b+c)/2 B
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