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45. II FIGURE P3.45 shows four electric charges located at the corners of a rectangle. Like charges, you will recall, repel each other while opposite charges attract. Charge B exerts a repulsive force (directly away from B) on charge A of $3.0\text{N}$. Charge C exerts an attractive force (directly toward C) on charge A of $6.0\text{N}$. Finally, charge D exerts an attractive force of $2.0\text{N}$on charge A. Assuming that forces are vectors, what are the magnitude and direction of the net force${\stackrel{→}{F}}_{\text{net}}$ exerted on charge A?

How would you define the zero vector$\stackrel{→}{0}?$

5. I A position vector in the first quadrant has an x-component of 6m and a magnitude of 10m . What is the value of its y-component?

6. I Draw each of the following vectors. Then find its - and components.

a.$\stackrel{→}{a}=\left(3.5\text{m}/{\text{s}}^2\right.$, negative x-direction)

b.$\stackrel{→}{v}=\left(440\text{m}/\text{s},{30}^{°}\right.$below the positive x-axis )

c.$\stackrel{→}{r}=\left(12\text{m},{40}^{°}\right.$ above the positive x-axis )

Can a vector have a component equal to zero and still have nonzero magnitude? Explain.

7. Draw each of the following vectors. Then find its x - and y- components.

a. $\stackrel{→}{v}=\left(7.5\text{m}/\text{s},\text{ â¶Ä‰â¶Ä‰}{30}^{°}\right.$clockwise from the positive x-axis )

b. $\stackrel{→}{a}=\left(1.5\text{m}/{\text{s}}^2,\text{ â¶Ä‰â¶Ä‰}{30}^{°}\right.$above the negative x-axis )

c. $\stackrel{→}{F}=\left(50.0\text{N},\text{ â¶Ä‰â¶Ä‰}{36.9}^{°}\right.$counter clockwise from the positive y-axis )

Can a vector have zero magnitudes if one of its components is nonzero? Explain.

Let $\stackrel{→}{C}=\left(3.15m,{15}^{∘}abovethenegativex-axis\right)$and $\stackrel{→}{D}=\left(25.6m,{30}^{∘}totherightofthenegativey-axis\right).$ Find the $x$- and $y$-components of each vector.

Suppose two vectors have unequal magnitudes. Can their sum be zero? Explain.

Let $\stackrel{→}{C}=\left(3.15\text{m},{15}^{°}\right.$above the negative $x$-axis ) and $\stackrel{→}{D}=$$\left(25.6\text{m},{30}^{°}\right.$ to the right of the negative $y$-axis). Find the $x$-and -$y$components of each vector.