Question

If for vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ , $\overrightarrow{a}+\overrightarrow{b}\ne \overrightarrow{0}$ and $\overrightarrow{c}$ is a non zero vector , then $(\overrightarrow{a}+\overrightarrow{b})\times [\overrightarrow{c}-(\overrightarrow{a}+\overrightarrow{b})]$ is

• A. $\overrightarrow{a}+\overrightarrow{b}$
• B. $(\overrightarrow{a}+\overrightarrow{b})\times \overrightarrow{c}$
• C. $\lambda ,\overrightarrow{c}$ where $\lambda$ is a non scalar
• D. $\lambda (\overrightarrow{a}+\overrightarrow{b}),\lambda \ne 0,1,$ a scalar

Answer 1

Answer: (B)

$\left(\vec{a}+\vec{b}\right)\times \left(\vec{c}-\left(\vec{a}+\vec{b}\right)\right)$
$=\left(\vec{a}+\vec{b}\right)\times \vec{c}-\left(\vec{a}+\vec{b}\right)\times \left(\vec{a}+\vec{b}\right)$
$=\left(\vec{a}+\vec{b}\right)\times \vec{c}$