Question

If $\alpha, \beta$ are vectors in an inner product space V, then

• A. $||\alpha + \beta||^{2} < ||\alpha||^{2} + ||\beta||^{2}$
• B. $||\alpha + \beta||^{2} = ||\alpha||^{2} + ||\beta||^{2}$
• C. $||\alpha + \beta||^{2} \le ||\alpha||^{2} + ||\beta||^{2}$
• D. $||\alpha + \beta||^{2} = ||\alpha - \beta||^{2}$

Hint:

The shortest distance between two points is a straight line. Any other path ($\alpha + \beta$) is always longer or equal.

Answer 1

The Correct Option is C