Triangle Inequality: True or False?

blinder
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Does the triangle inequality hold true for three vectors that says the norm(u+v+w)<=norm(u)+norm(v)+norm(w)...true or false
 
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true because norm(u+v+w) = norm( (u+v)+w)
<= norm(u+v) + norm(w)
<= (norm(u) + norm(v)) + norm(w)
<= norm(u) + norm(v) + norm(w)
 


True. The triangle inequality holds true for three vectors. This inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. In this case, the norm of u+v+w represents the length of the third side, while the norm of u, v, and w represent the lengths of the other two sides. Therefore, the inequality holds true and can be applied to three vectors.
 

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