List of top Physics Questions on Scalars and vectors

Given \(\overrightarrow A\)x \(\overrightarrow B\) = \(\overrightarrow C\),
Where \(\overrightarrow A = x\hat i+y\hat j+3\hat k\), \(\overrightarrow B = y\hat î + x\hat j + 2\hat k\), \(\overrightarrow C=-5\hat î+5\hat k\) 
Find the value of x and y

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): A given vector \(\overrightarrow{F}\) is irrotational i.e.,\(\overrightarrow{\nabla} ×\overrightarrow{F}\) =0.
Reason (R): The vector \(\overrightarrow{F}\) is conservative.
In the light of the above statements, choose the most appropriate answer from the options given below.

What is the value of div \(\overrightarrow r\), if \(\overrightarrow r\) is the position vector of a particle?
\(\left (\overrightarrow r = x\hat i + y\hat j + z\hat k\right)\)