Question

Two non-zero vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane, another vector $\overrightarrow{C}$ lies outside this plane, then the resultant of these three vectors i.e. $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}$ is

• A. Can be zero.
• B. Cannot be zero.
• C. Lies in the plane containing $\overrightarrow{A}+\overrightarrow{B}$
• D. Lies in the plane containing $\overrightarrow{C}$

Answer 1

The correct option is B Cannot be zero.

Resultant of vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in the same plane in which $\overrightarrow{A}$ and $\overrightarrow{B}$ lie. So, it makes some angle with vector $\overrightarrow{C}$ which lies outside the plane. Hence, the resultant of these vectors cannot be zero and it can lie in between the plane containing resultant of vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ and plane containing vector $\overrightarrow{C}$