Vectors Question 56
Question: Assertion : If dot product and cross product of $ \vec{A} $ and $ \vec{B} $ are zero, it implies that one of the vector $ \vec{A} $ and $ \vec{B} $ must be a null vector. Reason : Null vector is a vector with zero magnitude.
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: B
Solution:
$ \vec{A}.\vec{B}=|\vec{A}||\vec{B}|\cos \theta =0 $
$ \vec{A}\times \vec{B}=|\vec{A}||\vec{B}|\sin \theta =0 $ If $ \vec{A} $ and $ \vec{B} $ are not null vectors then it follows that $ \sin \theta $ and $ \cos \theta $ both should be zero simultaneously. But it cannot be possible so it is essential that one of the vector must be null vector.
BETA
