Vector Algebra Question 359

Question: If q be the angle between two vectors a and b, then $ \mathbf{a}.\mathbf{b} $ $ \ge 0 $ if

[MP PET 1995]

Options:

A) $ 0\le \theta \le \pi $

B) $ \frac{\pi }{2}\le \theta \le \pi $

C) $ 0\le \theta \le \frac{\pi }{2} $

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • As we know $ \mathbf{a},.,\mathbf{b}=ab\cos \theta $ Obviously, $ \cos \theta ,\ge 0 $ for $ 0\le ,\theta \le \frac{\pi }{2} $ and $ \frac{3\pi }{2}\le ,\theta ,\le 2\pi . $