Question

The maximum and minimum magnitudes of the resultant of two vectors are 23 units and 7 units respectively. If these two vectors are acting at right angles to each other, the magnitude of their resultant will be

• A. $14\text{units}$
• B. $15\text{units}$
• C. $16\text{units}$
• D. $17\text{units}$

Answer 1

The correct option is D $17\text{units}$

Let us assume two vectors are $P$ and $Q$,
Maximum magnitude of the resultant vector is,
$P+Q=23\text{units}..........\left(1\right)$
And, Minimum magnitude of the resultant vector is,
$P-Q=7\text{units}..........\left(2\right)$
Adding equations $\left(1\right)$ and $\left(2\right)$, we get $P=15\text{units}$
Hence from equation $\left(1\right)$, $Q=23-15=8\text{units}$
If $\overrightarrow{P}\perp \overrightarrow{Q}$
Then magnitude of their resultant is,
$R=\sqrt{P^2+Q^2}=\sqrt{225+64}R=17\text{units}$