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Chapter 3: Q. 25 (page 78)

FIGURE $P 3.25$ shows vectors $\vec{A} & \vec{B}$ . Find vector $\vec{C}$ such that $\vec{A} + \vec{B} + \vec{C} = \vec{0}$ . Write your answer in component form.

Short Answer

Expert verified

The vector is $\vec{C} = - 10$ .

Step by step solution

Step 1. Given information

The following diagram is given

Step 2. The vectors

The vectors are

$\vec{A} = 4 \sin 30 + 4 \cos 60 = 4 \vec{B} = 3 \cos 20 + 3 \sin 70 = 6$

Therefore, the third vector is

$\vec{C} = - (6 + 4) = - 10$

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Most popular questions from this chapter

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?

Let $\vec{A} = 4 \hat{i} - 2 \hat{j}$ , $\vec{B} = - 3 \hat{i} + 5 \hat{j}$ and $C = A + B$ .

a. Write vector $\vec{C}$ in component form.

b. Draw a coordinate system and on it show vectors $\vec{A}, \vec{B}$ , and $\vec{C}$ .

c. What are the magnitude and direction of vector $\vec{C}$ ?

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 $3.0 N$ . Charge C exerts an attractive force (directly toward C) on charge A of $6.0 N$ . Finally, charge D exerts an attractive force of $2.0 N$ on charge A. Assuming that forces are vectors, what are the magnitude and direction of the net force ${\vec{F}}_{net}$ exerted on charge A?

Trace the vectors in FIGURE EX3.2 onto your paper. Then find

(a) $\vec{A} + \vec{B}$ and (b) $\vec{A} - \vec{B}$

Let $\vec{A} = (3.0 m, 20^{\circ} s o u t h o f e a s t), \vec{B} = (2.0 m n o r t h) a n d \vec{C} = (5.0 m, 70^{\circ} s o u t h o f w e s t) .$ a.Draw and label $\vec{A}, \vec{B} a n d \vec{C}$ with their tails at the origin. Use a coordinate system with the $x$ -axis to the east.

b. Write $\vec{A}, \vec{B} a n d \vec{C}$ in component form, using unit vectors.

c. Find the magnitude and the direction of $\vec{D} = \vec{A} + \vec{B} + \vec{C} .$

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FIGURE P3.25shows vectors A→&B→. Find vector C→such that A→+B→+C→=0→. Write your answer in component form.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The vectors

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FIGURE $P 3.25$ shows vectors $\vec{A} & \vec{B}$ . Find vector $\vec{C}$ such that $\vec{A} + \vec{B} + \vec{C} = \vec{0}$ . Write your answer in component form.