Adding Vectors by Components Video Lessons

Concept

# Problem: For the vectors shown in the figure, determinePart A. the magnitude of 2A − 3B + 2C. Express your answer using three significant figures.Part B. the direction of 2A − 3B + 2C. Express your answer using three significant figures.

###### FREE Expert Solution

2D vectors, Magnitude & Direction/Components:

$\overline{)\mathbf{|}\stackrel{\mathbf{⇀}}{\mathbit{A}}\mathbf{|}{\mathbf{=}}\sqrt{{{\mathbit{A}}_{\mathbit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbit{A}}_{\mathbit{y}}}^{\mathbf{2}}}}$

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

Part A.

θA = 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

θB = 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

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###### Problem Details

For the vectors shown in the figure, determine

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

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