Vector Related problem If vec(a),vec(b) &vec(c0 are unit vector such that |vec(a)−vec(b)|^2+|vec(b)-vec(c)|^2+|vec(c)−vec(a)∣^2=9. How do I proceed

Alisa Taylor 2022-10-16 Answered
If a , b & c are unit vector such that | a b | 2 + | b c | 2 + | c a | 2 = 9
Then the value | 2 a + 5 b + 5 c | = _ _ _ _ _ _
My approach is as follow
| a b | 2 + | b c | 2 + | c a | 2 = | a | 2 + | b | 2 2 a . b + | b | 2 + | c | 2 2 b . c + | c | 2 + | a | 2 2 c . a = 9
( a . b + b . c + c . a ) = 3 2
How do I proceed from here
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Answers (1)

Kristin Myers
Answered 2022-10-17 Author has 12 answers
For convenience we shall take a = a , b = b , c = c
by your work
a b + b c + c a + 3 2 = 0
| a + b + c | 2 = 0
| a + b + c | = 0
a + b + c = 0
| 2 a + 5 b + 5 c | = | 2 a 5 a | = 3
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