Question

The maximum and minimum magnitude of the resultant of two given vectors are 17 units and 7 unit 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

Answer: (D)

13

Answer 2

$R_{\max}$ when $\theta = 0{^\circ}$

$R_{\min}$ when $\theta = 180{^\circ}$

By solving we get $A = 12$ and $B = 5$

Now when $\theta = 90{^\circ}$ then $R = \sqrt{A^{2} + B^{2}}$

⇒$R = \sqrt{(12)^{2} + (5)^{2}} = \sqrt{169} = 13$