Question

The vector $\vec{a}\times (\vec{b}\times \vec{c}$ ) is:

• A. parallel to $\overrightarrow{a}$
• B. perpendicular to $\vec{a}$
• C. parallel to $\overrightarrow{b}$
• D. perpendicular to $\vec{b}$

Answer 1

Answer: (A)

Consider $\vec{a}\times (\vec{w}b\times \vec{c})=(\overrightarrow{a\cdot c}]\vec{b}+(\vec{a}\cdot \vec{w}b)\vec{c}$
$\Rightarrow \bar{a}\times (\bar{b}\times \bar{c})$ lie in the plane of $\bar{b}$ and $\bar{c}$ which is parallel to $\vec{a}$.