3. Vectors

Let A = 4i - 2j, B = -3i + 5j, and C = A + B. What are the magnitude and direction of vector C?

Four forces are exerted on the object shown in FIGURE $P3.45$. (Forces are measured in newtons, abbreviated $\text{N}$.) The net force on the object is ${\vec{F}}_{\text{net}}={\vec{F}}_1+{\vec{F}}_2+{\vec{F}}_3+{\vec{F}}_4=4.0\hat{i}\text{N}$. What are (a) ${\vec{F}}_3$ and (b) ${\vec{F}}_4$? Give your answers in component form.

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. What are the magnitude and direction of vector F?

Let A = 4i - 2j, B = -3i + 5j, and C = A + B. Write vector C in component form.

(II) For the vectors shown in Fig. 3–41, determine

(b) 2 A (→ above A) ― 3 B (→ above B) + 2 C (→ above C) , and

(II) Three vectors are shown in Fig. 3–41. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with the +𝓍 axis.

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Figure 3–39 shows two vectors, $\overrightarrow{A}$ and $\overrightarrow{B}$, whose magnitudes are A = 6.8 units and B = 5.5 units. Determine $\overrightarrow{C}$ if $\overrightarrow{C}$ = $\overrightarrow{A}$ + $\overrightarrow{B}$. Give the magnitude and direction for each.

Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. Draw a coordinate system and on it show vectors A, B, and F.

Use components to determine the magnitude and direction of G = E＋F.

Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction.

$\overrightarrow{a}=(20i+10j){\text{m/s}}^2$

The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand in each case? Use a coordinate system in which the y-axis points toward the 12 on the watch face. From 8:00 to 8:20 a.m.

FIGURE P3.46 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 F_net exerted on charge A?

The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand in each case? Use a coordinate system in which the y-axis points toward the 12 on the watch face. From 8:00 to 9:00 a.m.