First slide

Scalar triple product of vectors

Question

If $\vec{a}, \vec{b} and \vec{c}$ are non-coplanar vectors $\vec{a} \times \vec{c}$ is perpendicular to $\vec{a} \times (\vec{b} \times \vec{c})$ then the value of $[\vec{a} \times (\vec{b} \times \vec{c})] \times \vec{c}$ is equal to

Moderate

A

$[\vec{a} \vec{b} \vec{c}] \vec{c}$
B

$[\vec{a} \vec{b} \vec{c}] \vec{b}$
C

$- [\vec{a} \vec{b} \vec{c}] \vec{a}$
D

$\vec{0}$

Solution

Given that $\vec{a}, \vec{b} and \vec{c}$ are non-coplanar vectors Thus,
$[\vec{a} \vec{b} \vec{c}] \neq 0 - - - - (i)$
$\begin{array}{l} again \vec{a} \times (\vec{b} \times \vec{c}) \cdot (\vec{a} \times \vec{c}) = 0 \\ or [(\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c}] \cdot (\vec{a} \times \vec{c}) = 0 \\ or (\vec{a} \cdot \vec{c}) [\vec{b} \vec{a} \vec{c}] = 0 \\ or (\vec{a} \cdot \vec{c}) = 0 \end{array}$
$Hence, \vec{a} and \vec{c} are perpendicular. --- (i i)$
$\begin{aligned} \vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c} \\ or [\vec{a} \times (\vec{b} \times \vec{c})] \times \vec{c} = \vec{0} \end{aligned}$

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