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

Addyson Bright

Addyson Bright

Answered question

2022-09-14

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.

Answer & Explanation

Katelyn Ryan

Katelyn Ryan

Beginner2022-09-15Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?