How to find the resultant of a set of vectors which lie in a figure resembling a kite?

Jun 2017
352
6
Lima, Peru
The problem is as follows:

Find the modulus of the resultant in centimeters from the set of vectors shown. The modulus of the vector $\left\|\vec{C}\right\|=6\,cm$. Consider that the segment $\overline{QT}=\overline{TS}$ (same in length) and that $QR=RS$.



$\begin{array}{ll}
1.&\sqrt{19}\,cm\\
2.&\sqrt{79}\,cm\\
3.&\sqrt{95}\,cm\\
4.&\sqrt{193}\,cm\\
5.&\sqrt{211}\,cm\\
\end{array}$

I'm stuck at this problem at exactly how to find the modulus of the resultant. All the alternatives are shown as square roots. But I don't know how does it appear? How exactly can I relate the lengths which are given? Can somebody help me here?
 

skeeter

Math Team
Jul 2011
3,292
1,776
Texas
$R_x = A_x+B_x+C_x = 7$

$R_y = A_y+B_y+C_y = -12$

$|A+B+C| = \sqrt{R_x^2 + R_y^2}$