Question

Name of the inequality \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) is:

• A. Cauchy-Schwartz Inequality
• B. Triangle Inequality
• C. Rolle's Inequality
• D. Lagrange's Inequality

Hint:

The Triangle Inequality is a fundamental property in vector algebra that applies to any two vectors.

Answer 1

The Correct Option is B

Step 1: Understanding the Triangle Inequality.
The inequality \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) is called the **Triangle Inequality**. It describes the relationship between the sides of a triangle, where the length of any side is always less than or equal to the sum of the lengths of the other two sides. This property is also true for vectors in a vector space. Step 2: Conclusion.
Thus, the correct answer is the **Triangle Inequality**, corresponding to option (B).