Question

The maximum and minimum magnitude of the resultant of two vectors are $23$ units and $7$ units respectively. Then the magnitude of the resultant vector when they act perpendicular to each other is

• A. $14$
• B. $15$
• C. $16$
• D. $17$

Answer 1

The correct option is D $17$

Let magnitude of the two vectors be $P$ and $Q$, it is given that the maximum and the minimum magnitude of the resultant are $23$ units and $7$ units respectively.

Hence,

$R_{max}=P+Q=\mathrm{23..........}\left(1\right)$,
(when both vectors $P$ and $Q$ are in the same direction or parallel)
$R_{min}=P-Q=7..........\left(2\right)$,
(when both vectors $P$ and $Q$ are in the opposite direction or Anti-parallel)

Adding $\left(1\right)$ and $\left(2\right)$
$\therefore 2P=30\Rightarrow P=15\therefore Q=23-15=8$

Now if $\overrightarrow{P}\perp \overrightarrow{Q},R=\sqrt{P^2+Q^2}=\sqrt{225+64}=17$

Hence option D is the correct answer