First slide

Vector triple product

Question

If $4 \vec{a} + 5 \vec{b} + 9 \vec{c} = 0, then (\vec{a} \times \vec{b}) \times [(\vec{b} \times \vec{c}) \times (\vec{c} \times \vec{a})] is equal to$

Moderate

A

a vector perpendicular to the plane of $\vec{a}, \vec{b} and \vec{c}$
B

a scalar quantity
C

$\vec{0}$
D

none of these

Solution

$\begin{array}{l} 4 \vec{a} + 5 \vec{b} + 9 \vec{c} = 0 \\ \Rightarrow Vectors \vec{a}, \vec{b} and \vec{c} are coplanar. \\ \Rightarrow \vec{b} \times \vec{c} and \vec{c} \times \vec{a} are collinear \\ \Rightarrow (\vec{b} \times \vec{c}) \times (\vec{c} \times \vec{a}) = \vec{0} \end{array}$

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