Question

If $\overline{a},\overline{b},\overline{c}$ are three non-zero vectors and $\overline{a}\ne \overline{b}$, $\overline{a}\times \overline{c}=\overline{b}\times \overline{c}$, then

• A. $\overline{a}-\overline{b}$ is parallel to $\overline{c}$
• B. $\overline{a}-\overline{b}$ is perpendicular to $\overline{c}$
• C. $\overline{a}+\overline{b}$ is parallel to $\overline{c}$
• D. $\overline{a}+\overline{b}$ is perpendicular to $\overline{c}$

Answer 1

Answer: (A)

$\overline{a}-\overline{b}$ is parallel to $\overline{c}$

We get

$(\overrightarrow{a}-\overrightarrow{b})\times \overrightarrow{c}=0$
So $(\overrightarrow{a}-\overrightarrow{b})\parallel \overrightarrow{c}$