Find |2a+3b+2 sqrt(3)(a xx b)| where a,b are perpendicular unit vectors.

Addyson Bright 2022-09-14 Answered
Find | 2 a + 3 b + 2 3 ( a × b ) | where a,b are perpendicular unit vectors.
My attempt:
( | 2 a + 3 b + 2 ( 3 ) ( a × b ) | ) 2
( a . b = 0 , | a | = | b | = 1 ) , n ^ is normal vector to a and b.
4 + 9 + 12 + 8 3 ( ± 1 ) + 12 3 ( ± 1 ) 25 ± 8 3 ± 12 3 | I have to eliminate one case 25 20 3 and then my answer should be ( 25 + 20 ( 3 ) 1 / 2 ) 1 / 2 or ( 25 + 4 ( 3 ) 1 / 2 ) 1 / 2 or ( 25 4 ( 3 ) 1 / 2 ) 1 / 2
Is this right way to solve the problem. I am given only one place to anwer and I have found three answers.
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Answers (1)

Katelyn Ryan
Answered 2022-09-15 Author has 11 answers
{ a , b , a × b } is an orthogonal set in R 3 so the Pythagorean theorem gives:
| 2 a + 3 b + 2 3 ( a × b ) | 2 = | 2 a | 2 + | 3 b | 2 + | 2 3 ( a × b ) | 2 = 4 + 9 + 12 = 25
Hence | 2 a + 3 b + 2 3 ( a × b ) | = 5

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