Question

TRIGONOMETRY (adding vectors algebraically)Find the magnitude of the resultant vector

Answer 1

Recall that the magnitude of a vector (x,y) is given by the following expression:

$\sqrt[]{x^2+y^2}\text{.}$

Also, recall that:

$(x,y)+(v,w)=(x+v,y+w)\text{.}$

Therefore, the resultant vector of the given diagram is:

$(14-9,7-2)=(5,5)\text{.}$

The magnitude of the above vector is:

$\begin{gathered} \sqrt[]{5^2+5^2}=\sqrt[]{2\cdot5^2}=5\sqrt[]{2} \\ \approx7.1. \end{gathered}$

Answer: 7.1.