Problem: 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  = 3.00A −4.00B  .d) Find the magnitude of  C .e) Find the direction of  C .

FREE Expert Solution

Vector components:

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

Magnitude:

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

Direction:

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

a)

A_x = (3.60) cos 70° = 1.23m