Question

The resultant of the two vectors having magnitude $2$ and $3$ is $1$. What will be their cross product?

• A. $6$
• B. $3$
• C. $1$
• D. $0$

Answer 1

The correct option is D $0$

$R=\sqrt{a^2+b^2+2ab\cos \theta }$
According to question, we are given that
$1=\sqrt{2^2+3^2+2\times 2\times 3\cos \theta }$
$1=4+9+12\cos \theta$
$\Rightarrow \cos \theta =-1$
$\Rightarrow \theta =\pi$
$\therefore |\overrightarrow{a}\times \overrightarrow{b}|=ab\sin \theta =0$