First slide

Vector triple product

Question

If $\vec{a} and \vec{b}$ are two unit vectors inclined at an angle $\frac{π}{3}$ then ${\vec{a} \times (\vec{b} + \vec{a} \times \vec{b})} \cdot \vec{b}$ is equal to

Moderate

A

$\frac{- 3}{4}$
B

$\frac{1}{4}$
C

$\frac{3}{4}$
D

$\frac{1}{2}$

Solution

$\begin{array}{l} {\vec{a} \times (\vec{b} + \vec{a} \times \vec{b})} \cdot \vec{b} \\ = {\vec{a} \times \vec{b} + \vec{a} \times (\vec{a} \times \vec{b})} \cdot \vec{b} \end{array}$
$\begin{array}{l} = [\vec{a} \vec{b} \vec{b}] + {(\vec{a} \cdot \vec{b}) \vec{a} - (\vec{a} \cdot \vec{a}) \vec{b}} \cdot \vec{b} \\ = 0 + (\vec{a} \cdot \vec{b})^{2} - (\vec{a} \cdot \vec{a}) (\vec{b} \cdot \vec{b}) \\ = \cos^{2} \frac{π}{3} - 1 = - \frac{3}{4} \end{array}$

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