Let C = A + B . - Vidyadip

MCQ

Let $\overrightarrow{\text{C}}=\overrightarrow{\text{A}}+\overrightarrow{\text{B}}.$

A
$|\overrightarrow{\text{C}}|$ is always greater than $|\overrightarrow{\text{A}}|$
✓
It is possible to have $|\overrightarrow{\text{C}}|<|\overrightarrow{\text{A}}|$ and $|\overrightarrow{\text{C}}|<|\overrightarrow{\text{B}}|$
C
C is always equal to A + B
D
C is never equal to A + B.

✓

Answer

Correct option: B.

It is possible to have $|\overrightarrow{\text{C}}|<|\overrightarrow{\text{A}}|$ and $|\overrightarrow{\text{C}}|<|\overrightarrow{\text{B}}|$

Explanation:

Statements (a), (c) and (d) are incorrect.

Given $\overrightarrow{\text{C}}=\overrightarrow{\text{A}}+\overrightarrow{\text{B}}$

Here, the magnitude of the resultant vector may or may not be equal to or less than the magnitudes of $\overrightarrow{\text{A}}$ and $\overrightarrow{\text{B}}$ or the sum of the magnitudes of both the vectors if the two vectors are in opposite directions.

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