Question

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

• A. $6$
• B. $3$
• C. $1$
• D. $0$

Answer 1

The correct option is D $0$

Let the two vectors be $\overrightarrow{a}$ and $\overrightarrow{b}$ and their resultant be $\overrightarrow{R}$.
Then magnitude of the resultant,
$R=\sqrt{a^2+b^2+2ab\cos \theta }$
$1=\sqrt{2^2+3^2+2\times 2\times 3\cos \theta }$
$1=4+9+12\cos \theta$
$\cos \theta =-1$
$\theta =\pi$
$|\overrightarrow{a}\times \overrightarrow{b}|=ab\sin \theta$
= 0