Question

If the edges of a parallelopiped are of unit length and are parallel to non - coplanar unit vectors $a,b$ and $c$ such that $a\cdot b=b\cdot c=c\cdot a=\frac{1}{2}$. Then, the volume of the parallelopiped is

• A. $\frac{1}{\sqrt{2}}$cu unit
• B. $\frac{1}{2\sqrt{2}}$cu unit
• C. $\frac{\sqrt{3}}{2}$ cu unit
• D. $\frac{1}{\sqrt{3}}$cu unit

Answer 1

The correct option is A $\frac{1}{\sqrt{2}}$cu unit

Volume of the paralleled is given by:-

$a.(b\times c).............\left(i\right)$

unit vectors are arranged at ${60}^0$ andle to each other so easily if we visualize the diagram b vector and c vector on 1 phase

so magnitude of the expressions (i) is

$\begin{array}{c}1\times \cos 45\\ =\frac{1}{\sqrt{2}}units\end{array}$