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7. Sara wants to show that (a × b) × ê ‡ à × (b × c). Yasmina says that it is impossible and comes up with three sets of vectors to prove Sara wrong. Do any of Yasmina's sets of vectors prove Sara's statement to be correct? Explain with words and math. [ i. a = (1,0,0), b = (0, 1, 0), c = (0,0,1) (1, 1,0), b = (1, −1,0), è = (0, 0, −1) iii. a = (1, 0, 0), b = (1, 1, 0), ¿ = (1, 1, 1) ii. à =

7. Sara wants to show that (a × b) × ê ‡ à × (b × c). Yasmina says that it is impossible and comes up with three sets of vectors to prove Sara wrong. Do any of Yasmina's sets of vectors prove Sara's statement to be correct? Explain with words and math. [ i. a = (1,0,0), b = (0, 1, 0), c = (0,0,1) (1, 1,0), b = (1, −1,0), è = (0, 0, −1) iii. a = (1, 0, 0), b = (1, 1, 0), ¿ = (1, 1, 1) ii. à =

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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Answer the question in the space provided and in full details.  Answer in compplete sentences, with words and with therefore statements. Use the the information already provided for you to answer the question in math terms words. Explain each statements. a is the question and the rest of the images are the answers.Thank you.

7. Sara wants to show that (a × b) × ê ‡ à × (b × c). Yasmina says that it is impossible and comes up with three sets of vectors to prove Sara wrong. Do any of Yasmina's sets of vectors prove Sara's statement to be correct? Explain with words and math. [ i. a = (1,0,0), b = (0, 1, 0), c = (0,0,1) (1, 1,0), b = (1, −1,0), è = (0, 0, −1) iii. a = (1, 0, 0), b = (1, 1, 0), ¿ = (1, 1, 1) ii. à =
Transcribed Image Text:7. Sara wants to show that (a × b) × ê ‡ à × (b × c). Yasmina says that it is impossible and comes up with three sets of vectors to prove Sara wrong. Do any of Yasmina's sets of vectors prove Sara's statement to be correct? Explain with words and math. [ i. a = (1,0,0), b = (0, 1, 0), c = (0,0,1) (1, 1,0), b = (1, −1,0), è = (0, 0, −1) iii. a = (1, 0, 0), b = (1, 1, 0), ¿ = (1, 1, 1) ii. à =
(ii) a = (1,1,0), B² = (1,-1,0), C = (0,0,-1) Now axb: 个子企 = 1 (0-0)-3 (0-0) + (-1-1) = = -2 k = (0,0,-2) Now (axb)xc R = Now bx c î(1-0)-3(-1-0) + (0-0) (1,1₂0) î Ĵ ax (√x c) = = fence (@²x b)x= = ax(5x) → Sara's statement is not correct. (ii) a = (10,0), B² = (1,1,0), ² = (1, 1, 1) 9 î 1 ả xổ = 1 O 1 (0-0)-3 (0-0) + (1-0) = = (0,0,1) ↑ J K î cả XE) xã î (0-1)-1 (0-1) +R (0-0) (-1,1,0) = bxc = | 1 1 K -î (1-0)-3(1-0) + ^ (1-1) = (1₁-1₂0) ax(bxc) 소 Ĵ F = 1 -1 = ↑ (0-0)-1 (0-0) + (-1-0) -K (0,0,-1) ax(bx2) + (axb) x c Sara's statement is true for these vectors. We have to Check (axb)x2 + ax(x) i) a = (1,0,0) ₂7² = (0,1,0), c²= (0,0,1) ả xổ M Now (axb) x 2 = bxc Now Now ax (x²) => (axb) x 2 Sara's statement = 2- 0 - = N 701 ۲۲ - - <200 î ਕਿ 13 = = ㅇㅇ) = من K 17 & 8 ) = î (0-0)-1 (0-0) + (1-0) 0 R N = (0,0,1) = ↑ Ĵ K 1 = 0 î Ĵ k = | |-^ 2 ^(1-0)-1 (0-0)+ (0-0) ↑ - = (1,0,0) 소소 소 ax(x2) not correct here.
Transcribed Image Text:(ii) a = (1,1,0), B² = (1,-1,0), C = (0,0,-1) Now axb: 个子企 = 1 (0-0)-3 (0-0) + (-1-1) = = -2 k = (0,0,-2) Now (axb)xc R = Now bx c î(1-0)-3(-1-0) + (0-0) (1,1₂0) î Ĵ ax (√x c) = = fence (@²x b)x= = ax(5x) → Sara's statement is not correct. (ii) a = (10,0), B² = (1,1,0), ² = (1, 1, 1) 9 î 1 ả xổ = 1 O 1 (0-0)-3 (0-0) + (1-0) = = (0,0,1) ↑ J K î cả XE) xã î (0-1)-1 (0-1) +R (0-0) (-1,1,0) = bxc = | 1 1 K -î (1-0)-3(1-0) + ^ (1-1) = (1₁-1₂0) ax(bxc) 소 Ĵ F = 1 -1 = ↑ (0-0)-1 (0-0) + (-1-0) -K (0,0,-1) ax(bx2) + (axb) x c Sara's statement is true for these vectors. We have to Check (axb)x2 + ax(x) i) a = (1,0,0) ₂7² = (0,1,0), c²= (0,0,1) ả xổ M Now (axb) x 2 = bxc Now Now ax (x²) => (axb) x 2 Sara's statement = 2- 0 - = N 701 ۲۲ - - <200 î ਕਿ 13 = = ㅇㅇ) = من K 17 & 8 ) = î (0-0)-1 (0-0) + (1-0) 0 R N = (0,0,1) = ↑ Ĵ K 1 = 0 î Ĵ k = | |-^ 2 ^(1-0)-1 (0-0)+ (0-0) ↑ - = (1,0,0) 소소 소 ax(x2) not correct here.
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