2D vectors, Magnitude & Direction/Components:

$\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{A}}_{\mathit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{A}}_{\mathit{y}}}^{\mathbf{2}}}}$

$\overline{){\mathbf{tan}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{A}}_{\mathit{y}}}{{\mathit{A}}_{\mathit{x}}}}$

$\overline{)\begin{array}{rcl}{\mathit{A}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathit{\theta}\\ {\mathit{A}}_{\mathit{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathit{\theta}\end{array}}$

**Part**** A.**

θ_{A} = 28.0°

A = Acosθ i - Asinθ j = 44.0cos28.0 i + 44.0sin28.0 j = 38.8 i + 20.7 j

2A = 2(38.8 i + 20.7 j) = 77.6 i + 41.4 j

θ_{B} = 180.0 - 56.0 = 124.0°

B = Bcosθ i - Bsinθ j = 26.5cos124.0 i + 26.5sin124.0 j = -14.8 i + 22.0 j

For the vectors shown in the figure, determine

Part A. the magnitude of 2*A *− 3*B *+ 2*C*. Express your answer using three significant figures.

Part B. the direction of 2*A *− 3*B *+ 2*C*. Express your answer using three significant figures.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Adding Vectors by Components concept. You can view video lessons to learn Adding Vectors by Components. Or if you need more Adding Vectors by Components practice, you can also practice Adding Vectors by Components practice problems.