3. Vectors

Adding Vectors by Components

Open Question
A crate, seen from above, is pulled with three ropes that have the tensions shown in FIGURE P3.44. Tension is a vector directed along the rope, measured in newtons (abbreviated N). Suppose the three ropes are replaced with a single rope that has exactly the same effect on the crate. What is the tension in this rope? Write your answer in component form using unit vectors.
Open Question
Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction. (b) r = (-2.0i - 1.0j) cm
Open Question
Draw each of the following vectors, label an angle that specifies the vector's direction, then find its magnitude and direction. (a) B = -4.0i + 4.0j
Open Question
Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction. (c) v = (14i - 11j) m/s
Open Question
Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction. (a) A = 3.0i + 7.0j
Open Question
Let A = (3.0 m, 20° south of east), B = (2.0 m, north), and C = (5.0 m, 70° south of west).c. Find the magnitude and the direction of D = A＋B＋C.
Open Question
Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. (a) Write vector F in component form.
Open Question
Let A = 4i - 2j, B = -3i + 5j, and E = 2A + 3B. (c) What are the magnitude and director of vector E?
Open Question
Let A = 4i - 2j, B = -3i + 5j, and C = A + B. (c) What are the magnitude and director of vector C?
Open Question
Four forces are exerted on the object shown in FIGURE P3.45. (Forces are measured in newtons, abbreviated N.) The net force on the object is Fₙₑₜ = F₁ + F₂ + F₃ + F₄ = 4.0î N. What are (a) F₃ and (b) F₄? Give your answers in component form.
Open Question
Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. (c) What are the magnitude and director of vector F?
Open Question
Let A = 4i - 2j, B = -3i + 5j, and C = A + B. (a) Write vector C in component form.
Open Question
(II) For the vectors shown in Fig. 3–41, determine

(b) 2 A (→ above A) ― 3 B (→ above B) + 2 C (→ above C) , and
Open Question
(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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Open Question
(II) Figure 3–39 shows two vectors, A (→ above A) and B (→ above B) , whose magnitudes are A = 6.8 units and B = 5.5 units. Determine C (→ above C) if
(a) C(→ above C) = A (→ above A) + B (→ above B) ,
Give the magnitude and direction for each.

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