First slide

Scalar triple product of vectors

Question

If $\vec{d} = \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}$ is a non-zero vector and $∣ (\vec{d} \cdot \vec{c}) (\vec{a} \times \vec{b}) + (\vec{d} \cdot \vec{a}) (\vec{b} \times \vec{c})$ $+ (\vec{d} \cdot \vec{b}) (\vec{c} \times \vec{a}) ∣= 0$ then

Moderate

A

$| \vec{a} | = | \vec{b} | = | \vec{c} |$
B

$| \vec{a} | + | \vec{b} | + | \vec{c} | = | \vec{d} |$
C

$\vec{a}, \vec{b} and \vec{c}$ are coplanar
D

none of these

Solution

$\begin{array}{l} \vec{d} \cdot \vec{c} = \vec{d} \cdot \vec{b} = \vec{d} \cdot \vec{c} = [\vec{a} \vec{b} \vec{c}] \\ Then ∣ (\vec{d} \cdot \vec{c}) (\vec{a} \times \vec{b}) + (\vec{d} \cdot \vec{a}) (\vec{b} \times \vec{c}) + (\vec{d} \cdot \vec{b}) (\vec{c} \times \vec{a}) ∣= 0 \\ or [\vec{a} \vec{b} \vec{c}] | \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} | = 0 \\ or [\vec{a} \vec{b} \vec{c}] = 0 (∵ \vec{d} is non-zero) \end{array}$

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