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If a=3,b=4,c=5 and a+b+c=0 then angle between a and b is

If a=3,b=4,c=5 and a+b+c=0 then angle between a and b is

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear pallavi

|a|=3,|b|=4,|c|=5

 a+b+c=0

 a+b =-c

|a+b| =|-c|

|a+b|2 =|-c|2

|a|2 +|b|2 +2a.b =|c|2

 9  + 16  +2a.b= 25

a.b=0

 so a and b are perpendicular

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Kushagra Madhukar
askIITians Faculty 629 Points
2 years ago
Dear student,
Please find the solution to your problem.
 
|a| = 3, |b| = 4, |c| = 5
a + b + c = 0
a + b = – c
|a + b| = | – c|
|a + b|2 = | – c|2
|a|2 + |b|2 + 2a.b = |c|2
9  + 16  + 2a.b = 25
a.b = 0
so a and b are perpendicular.
 
Thanks and regards,
Kushagra

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