Question

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

• A. greater than $(a+b)$
• B. not greater than $(a+b)$
• C. equal to $(a+b)$
• D. less than $(a+b)$

Answer 1

The correct option is B not greater than $(a+b)$

$|\overrightarrow{a}+\overrightarrow{b}|\le |\overrightarrow{a}|+|\overrightarrow{b}|i.e.|\overrightarrow{a}+\overrightarrow{b}|\le a+b$