Vector Algebra Question 334
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
[UPSEAT 2001]
Options:
A) 0
B) $ \pi /2 $
C) 1
D) $ \pi /4 $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ |\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 $ , $ [\because |\mathbf{x}{{|}^{2}}=,|\mathbf{y}{{|}^{2}}=1,|\mathbf{x}|,=,|\mathbf{y}|=1] $ .
BETA
