Question

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

• 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

• Since the third vector $\overrightarrow{C}$ has a component which lies outside the plane of the remaining two, hence this extra component can not be cancelled by any other component during addition, so Resultant can never be zero.
• Also, the Resultant lies outside the plane of $\overrightarrow{A}+\overrightarrow{B}$ because of this extra component of $\overrightarrow{C}$
• Hence option B is correct