Question

Assertion :Statement-I : The angle between vectors $\overrightarrow{A}\times \overrightarrow{B}$ and $\overrightarrow{B}\times \overrightarrow{A}$ is $\pi$ radian.
Because Reason: Statement-II : $\overrightarrow{B}\times \overrightarrow{A}=-\overrightarrow{A}\times \overrightarrow{B}$

• A. Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
• B. Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I.
• C. Statement-I is true, Statement-II is false.
• D. Statement-I is false, Statement-II is true.

Answer 1

The correct option is A Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.

$\overrightarrow{B}\times \overrightarrow{A}$ $=AB\sin \theta$

$=AB\sin (\pi -\theta )=AB[\sin \pi \cos \theta -\cos \pi \sin \theta ]$

$=AB[0-1(\sin \theta \left)\right]=-AB\sin \theta =-\overrightarrow{A}\times \overrightarrow{B}$