If $\vec{a}$ and $\vec{b}$ are two non zero vectors, then which of the following is correct :
A. $\vec{a}×\vec{b}=\vec{0}$ if and only if $\vec{a}$ is perpendicular to $\vec{b}$.
B. $\vec{a}×\vec{b}$ is vector.
C. $\vec{a}×\vec{b}=|\vec{a}||\vec{b}|cos\theta \hat{n}$
D. If $\theta =\frac{\pi}{2} , |\vec{a}×\vec{b}|=|\vec{a}||\vec{b}|$
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is option (4) → B and D only
A. $\vec{a}×\vec{b}=ab\hat n$ (NOT $\vec 0$)
B. True
C. False, $\vec{a}×\vec{b}=|\vec{a}||\vec{b}|\sin θ\hat n$ (NOT $\cos θ$)
D. True
Only B, D True