Question

The maximum and minimum magnitudes of the resultant of two given vectors are 17 units and 7 units respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

• A. 14
• B. 16
• C. 18
• D. 13

Answer 1

The correct option is D 13

$R_{max}$ = A + B = 17 when $\theta$ = $0^{\circ }$
$R_{min}$ = A - B = 7 when $\theta$ = ${180}^{\circ }$
by solving we get A = 12 and B = 5
Now when $\theta$ = ${90}^{\circ }$ then R = $\sqrt{A^2+B^2}$
$\Rightarrow$R=$\sqrt{{\left(12\right)}^2+{\left(5\right)}^2}$ = $\sqrt{169}$ = 13