Question 29

Mathematics Scalar and Vector Products Medium

If \(\theta(0 \leq \theta \leq \pi)\) is the angle between the vectors \(\bar{a}\) and \(\bar{b}\), then \(\frac{|\bar{a} \times \bar{b}|}{\bar{a} \cdot \bar{b}}\) equals

(A) \(-\cot \theta\)
(B) \(\tan \theta\)
(C) \(-\tan \theta\)
(D) \(\cot \theta\)
View Dynamic Solution & Explanation
Correct Solution: Option B

Step-by-step Solution:

We know that \(\frac{|\vec{a} \times \vec{b}|}{\vec{a} \bullet \vec{b}}=\frac{|\vec{a}||\vec{b}| \sin \theta}{|\vec{a}||\vec{b}| \cos \theta}=\tan \theta\) Choice (B)