3. Vectors

While vacationing in the mountains you do some hiking. In the morning, your displacement is $\(\mathbf{S}\)_{morning} = (2000 \, \(\text{m}\), \(\text{east}\)) + (3000 \, \(\text{m}\), \(\text{north}\)) + (200 \, \(\text{m}\), \(\text{vertical}\))$. Continuing on after lunch, your displacement is $\(\mathbf{S}\)_{afternoon} = (1500 \, \(\text{m}\), \(\text{west}\)) + (2000 \, \(\text{m}\), \(\text{north}\)) - (300 \, \(\text{m}\), \(\text{vertical}\))$. What is the magnitude of your net displacement for the day?

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

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

(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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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 E = 2A + 3B. What are the magnitude and direction of vector E?

Which of the following operations will not change a $\mathrm{vector}$?

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

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 8:20 a.m.

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.

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

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.