Question

Vector $\stackrel{\rightharpoonup }{A}$ has a magnitude of $5units$ lies in the $XY-$ plane and points in a direction $120°$ from the direction of increasing $x$. Vector $\stackrel{\rightharpoonup }{B}$ has a magnitude of $9units$ and points along the $z-$axis. The magnitude of cross product $\stackrel{\rightharpoonup }{A}\times \stackrel{\rightharpoonup }{B}$ is

• A. $30$
• B. $35$
• C. $40$
• D. $45$

Answer 1

The correct option is D

$45$

Explanation for the correct option:

Given that $\left|\stackrel{\rightharpoonup }{A}\right|=5$, $\left|\overrightarrow{B}\right|=9$

From the figure we can see that

Vector $\stackrel{\rightharpoonup }{B}$ makes an angle of $90°$ with vector $\stackrel{\rightharpoonup }{A}$ since $z-$ axis perpendicular to $XY-$plane

The magnitude of the cross product between these vectors is given as

$\left|\stackrel{\rightharpoonup }{A}\times \stackrel{\rightharpoonup }{B}\right|=\left|\stackrel{\rightharpoonup }{A}\right|\left|\stackrel{\rightharpoonup }{B}\right|\sin \left(\theta \right)$ where $\theta =90°$

Substituting all the values we get

$\Rightarrow$$\left|\stackrel{\rightharpoonup }{A}\times \stackrel{\rightharpoonup }{B}\right|=5\times 9\times \sin \left(90°\right)$

$\Rightarrow$$\left|\stackrel{\rightharpoonup }{A}\times \stackrel{\rightharpoonup }{B}\right|=45$

Hence, option(D) is the correct answer.