Help! Question on inequality and vectors.?

The triangle inequality is stated as follows: Given any two vectors u and v , ||u+v|| </= ||u||+||v||. Demonstrate this inequality.

note: there are vector symbols on top of the u and v. and the sign (</=) means smaller or equal to.

Any help will be appreciated.

Thank you!

1 Answer

  • 7 years ago
    Favorite Answer

    These "double absolute value signs" simply refer to the lengths of the vectors.

    And just like triangles made from line segments, you can't have the length of one side

    greater than the sum of the lengths of the other two sides.

    As long as you agree that the shortest distance between two points is a

    straight line, then any detour must be longer.

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