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 .

Vector components:

$\begin{array}{rcl} A_{x} & = & | \overset{⇀}{A} | \cos θ \\ A_{y} & = & | \overset{⇀}{A} | \sin θ \end{array}$

Magnitude:

$| \overset{⇀}{A} | = \sqrt{{A_{x}}^{2} + {A_{y}}^{2}}$

Direction:

$\tan θ = \frac{A_{y}}{A_{x}}$

A_x = (3.60) cos 70° = 1.23m

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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 .

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