Question

If the magnitudes of $\overrightarrow{A}$ and $\overrightarrow{B}$ are $a$ and $b$ respectively, the magnitude of the resultant vector is always:

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

Answer 1

Answer: (D)

not greater than $(a+b)$

Resultant of two vectors $R=\sqrt{a^2+b^2+2abcos\theta }$
$R$ will have maximum value when $cos\theta$ is maximum, that is $cos\theta =1$.
Then, $R$ becomes $a+b$, which is the resultant when $\overrightarrow{A}$ and $\overrightarrow{B}$ are in the same direction.
But, $R$ can never be greater than $a+b$.