Answer:
Explanation:
To find the sum of vector, (C=A+B)we can descompose each of the vectors in the x & y coordinates.
vector A
A=3.14;30°
[tex]A_{x} = 3.14*cos(30) = 2.71[m]\\A_{y} = 3.14*sin(30) = 1.57[m][/tex]
vector B
B=2.71;-60
[tex]B_{x} = 2.71*cos(60) = 1.355[m]\\B_{y} = - 2.71*sin(60) = -2.35[m]\\[/tex]
Now we can sum each of the coordinates:
C = A + B
[tex]C = (2.71+1.355)_{x} + (1.57-2.35)_{y} \\C = 4.065 i - 0.78 j[/tex]
Those are the components of the vector, to find its magnitude we can use Pythagoras.
[tex]C = \sqrt{(4.065)^{2} +(0.78)^{2} } \\C = 4.13 [m]\\\\[/tex]
And the angle will be:
[tex]tan(\alpha ) = \frac{0.78}{4.065} \\\alpha = 10.86 [deg] below the horizontal[/tex]
