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

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