Scalar product to prove triangle inequality?

[8emnero8]

Homework Statement

From the inequality

|a.b| <= |a||b|

prove the triangle inequality:

|a+b| <= |a| + |b|

Homework Equations

a.b = |a|b| cos theta

The Attempt at a Solution

Making a triangle where side c = a+b. Don't know how to approach the question.

Thanks.

 

[_h2tm]

I may not be understanding your question, but it seems like you should start with the Pythagorean Identities.

 

[zapz]

Also think about what values your trig function is between

 

[Dick]

You should start by knowing |a+b|^2=(a+b).(a+b). Now expand the right side.