Question

If x and y are two unit vectors and $\pi$ is the angle between them, then $\frac{1}{2}|x - y|$ is equal to

• A. 0
• B. $\pi/2$
• C. 1
• D. $\pi/4$

Answer 1

Answer: (C)

1

Answer 2

$|\mathbf{x} - \mathbf{y}|^{2} = (\mathbf{x} - \mathbf{y}).(\mathbf{x} - \mathbf{y}) = 1 + 1 - 2|\mathbf{x}||\mathbf{y}|\cos\pi$

=$2 - 2\cos\pi,\therefore\ |\mathbf{x} - \mathbf{y}|^{2} = 4$

So, $\frac{1}{2}|\mathbf{x} - \mathbf{y}| = 1$, $\lbrack\because|\mathbf{x}|^{2} = |\mathbf{y}|^{2} = 1,|\mathbf{x}| = |\mathbf{y}| = 1\rbrack$.