First slide

Scalar triple product of vectors

Question

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

Moderate

A

$\frac{1}{\sqrt{2}} cu units$
B

$\frac{1}{2 \sqrt{2}} cu units$
C

$\frac{\sqrt{3}}{2} cu units$
D

$\frac{1}{\sqrt{3}} cu units$

Solution

${[\bar{a} \bar{b} \bar{c}]}^{2} = |\begin{matrix} \bar{a} . \bar{a} & \bar{a} . \bar{b} & \bar{a} . \bar{c} \\ \bar{b} . \bar{a} & \bar{b} . \bar{b} & \bar{b}, \bar{c} \\ \bar{c} . \bar{a} & \bar{c} . \bar{b} & \bar{c} . \bar{c} \end{matrix}|$
= $|\begin{matrix} 1 & \frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & 1 & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2} & 1 \end{matrix}| = \frac{1}{2}$
$Volume of parallel piped = [\bar{a} \bar{b} \bar{c}] = \frac{1}{\sqrt{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App