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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
Yes, the Triangle Inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is always true for any triangle.
Yes, the Triangle Inequality can be false for degenerate triangles, which are triangles with one or more sides that have zero length. In these cases, the sum of the lengths of two sides may be equal to the length of the third side, leading to a false Triangle Inequality.
The Triangle Inequality is used to determine whether a set of three given side lengths can form a valid triangle. It is also used in proofs and theorems related to triangles, such as the Pythagorean Theorem.
No, the Triangle Inequality is specific to triangles and cannot be applied to other shapes. It is based on the unique properties and relationships of the sides and angles in a triangle.
If the Triangle Inequality is violated, it means that the given side lengths cannot form a valid triangle. This could lead to errors in calculations or proofs that involve the triangle.