Question

The ratio of maximum and minimum magnitude of the resultant of two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is $5:1$. Now, $|\overrightarrow{a}|$ is equal to?

• A. $|\overrightarrow{b}|$
• B. $2|\overrightarrow{b}|$
• C. $\frac{3}{2}|\overrightarrow{b}|$
• D. $4|\overrightarrow{b}|$

Answer 1

The correct option is C $\frac{3}{2}|\overrightarrow{b}|$

For maximum condition the magnitude of two vectors must be added and for minimum condition the magnitude of two

vectors must be subtracted.

From the provided option if we consider

$|\overrightarrow{a}|=\frac{3}{2}|\overrightarrow{b}|$

Now for maximum condition

$|\overrightarrow{a}|+|\overrightarrow{b}|=\frac{3}{2}|\overrightarrow{b}|+|\overrightarrow{b}|=\frac{5}{2}|\overrightarrow{b}|$

And for minimum condition

$|\overrightarrow{a}|-|\overrightarrow{b}|=\frac{3}{2}|\overrightarrow{b}|-|\overrightarrow{b}|=\frac{|\overrightarrow{b}|}{2}$

Now the ratio of maximum and minimum

$\frac{|\overrightarrow{a}|+|\overrightarrow{b}|}{|\overrightarrow{a}|-|\overrightarrow{b}|}=\frac{\frac{5|\overrightarrow{b}|}{2}}{\frac{|\overrightarrow{b}|}{2}}=\frac{5}{1}$