Kinematics Question 43
Question: Assertion : If q be the angle between $ \vec{A} $ and $ \vec{B} $ , then $ \tan \theta =\frac{\vec{A}\times \vec{B}}{\vec{A}.\vec{B}} $ Reason : $ \vec{A}\times \vec{B} $ is perpendicular to $ \vec{A}.\vec{B} $
Options:
A) If both assertion and reason are true and the reason is the correct explanation of the assertion.
B) If both assertion and reason are true but reason is not the correct explanation of the assertion.
C) If assertion is true but reason is false.
D) If the assertion and reason both are false.
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{\vec{A}\times \vec{B}}{\vec{A}.\vec{B}}=\frac{AB\sin \theta \ \hat{n}}{AB\cos \theta }=\tan \theta \ \hat{n} $ where $ \hat{n} $ it’s unit vector perpendicular to both $ \vec{A} $ and $ \vec{B} $ . However $ \frac{|\vec{A}\times \vec{B}|}{\vec{A}.\vec{B}}=\tan \theta $
