Question

When two vectors, $\overrightarrow{a}$ and $\overrightarrow{b}$ are added, the magnitude of the resultant vector is always

• A. Greater than $(|\overrightarrow{a}|+|\overrightarrow{b}|)$
• B. less than or equal to $(|\overrightarrow{a}|+|\overrightarrow{b}|)$
• C. less than $(|\overrightarrow{a}|+|\overrightarrow{b}|)$
• D. equal to $(|\overrightarrow{a}|+|\overrightarrow{b}|)$

Answer 1

The correct option is B less than or equal to $(|\overrightarrow{a}|+|\overrightarrow{b}|)$

We know that,
$|\overrightarrow{a}|+|\overrightarrow{b}|\ge |\overrightarrow{a}+\overrightarrow{b}|>|\overrightarrow{a}|-|\overrightarrow{b}|$
Hence, the magnitude of resultant vector is always less than or equal to $(|\overrightarrow{a}|+|\overrightarrow{b}|)$.