JEE MAIN - Mathematics (2002 - No. 28)
If $$\left| {\overrightarrow a } \right| = 4,\left| {\overrightarrow b } \right| = 2$$ and the angle between $${\overrightarrow a }$$ and $${\overrightarrow b }$$ is $$\pi /6$$ then $${\left( {\overrightarrow a \times \overrightarrow b } \right)^2}$$ is equal to :
$$48$$
$$16$$
$$\overrightarrow a $$
none of these
स्पष्टीकरण
$${\left( {\overrightarrow a \times \overrightarrow b } \right)^2} = {\left| {\overrightarrow a } \right|^2}{\left| {\overrightarrow b } \right|^2}\,\,{\sin ^2}{\pi \over 6}$$
$$ = 16 \times 4 \times {1 \over 4} = 16$$
$$ = 16 \times 4 \times {1 \over 4} = 16$$