Answer:
Magnitude 17.85 cm
Angle: 69.36 degrees
Explanation:
Analytical sum of vectors
We have the vector 1 with magnitude 12 cm and angle 45 degrees. We'll find its cartesian components by using
[tex]v1_x=12cos45^o=8.49\ cm[/tex]
[tex]v1_y=12sin45^o=8.49\ cm[/tex]
Now we find the components of v2
[tex]v2_x=8.5cos105^o=-2.2\ cm[/tex]
[tex]v2_y=8.5sin105^o=8.21\ cm[/tex]
To add both vectors, we add their components separately
[tex]\vec{v3}=\vec{v2}+\vec{v1}[/tex]
[tex]v3_x=v1_x+v2_x=8.49\ cm-2.2\ cm=6.29\ cm[/tex]
[tex]v3_y=v1_y+v2_y=8.49\ cm+8.21\ cm=16.7\ cm[/tex]
Magnitude of [tex]\vec{v3}[/tex]:
[tex]\left \| \vec{v3} \right \|=\sqrt{v3_x^2+v3_y^2}[/tex]
[tex]\left \| \vec{v3} \right \|=\sqrt{(6.29)^2+(16.7)^2}[/tex]
[tex]\left \| \vec{v3} \right \|=17.85\ cm[/tex]
Angle of [tex]\vec{v3}[/tex]:
[tex]\theta_3=atan\left ( \frac{16.7}{6.29} \right )=69.36^o[/tex]
