Vector components:

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

Magnitude:

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

Direction:

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

**a)**

A_{x} = (3.60) cos 70° = 1.23m

a) Write the vector **A** in the figure (Figure 1) in terms of the unit vectors **î** and **ĵ**.

b) Write the vector **B** in the figure in terms of the unit vectors **î** and **ĵ**.

c) Use unit vectors to express the vector **C** , where **C** = 3.00**A** −4.00**B** .

d) Find the magnitude of **C** .

e) Find the direction of **C** .

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