Question

Let $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$
(a) $\left|\overrightarrow{C}\right|$ is always greater than $\left|\overrightarrow{A}\right|$
(b) It is possible to have $\left|\overrightarrow{C}\right|$ < $\left|\overrightarrow{A}\right|$ and $\left|\overrightarrow{C}\right|$ < $\left|\overrightarrow{B}\right|$
(c) C is always equal to A + B
(d) C is never equal to A + B.

Answer 1

(b) It is possible to have $\left|\overrightarrow{C}\right|$ < $\left|\overrightarrow{A}\right|$ and $\left|\overrightarrow{C}\right|$ < $\left|\overrightarrow{B}\right|$

Statements (a), (c) and (d) are incorrect.
Given: $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$
Here, the magnitude of the resultant vector may or may not be equal to or less than the magnitudes of $\overrightarrow{A}$ and $\overrightarrow{B}$ or the sum of the magnitudes of both the vectors if the two vectors are in opposite directions.