3. Vectors

Adding Vectors by Components

Multiple Choice
Which of the following does not describe the process of adding vectors by components?
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Multiple Choice
Let $\overset{⇀}{A} = \hat{i} + 2.0 \hat{j}$ , $\overset{⇀}{B} = - 7.0 \hat{i}$ , and $\overset{⇀}{C} = 3.0 \hat{i} + \hat{j}$ . What is the direction of $\overset{⇀}{A} + \overset{⇀}{B} + \overset{⇀}{C}$ ? Express your answer in degrees counter clockwise from the positive x axis.
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Multiple Choice
Let $\overset{⇀}{A} = \hat{i} + 2.0 \hat{j}$ , $\overset{⇀}{B} = - 7.0 \hat{i}$ , and $\overset{⇀}{C} = 3.0 \hat{i} + \hat{j}$ . What is the magnitude of $\overset{⇀}{A} + \overset{⇀}{B} + \overset{⇀}{C}$ ?
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Textbook Question
A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.
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Textbook Question
For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference B - A

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Textbook Question
For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector difference A - B

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Textbook Question
For the vectors A and B in Fig. E1.24 use the method of components to find the magnitude and direction of the vector sum A + B

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Textbook Question
FIGURE P3.43 shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. How hard and in what direction must you pull on the third rope to keep the knot from moving? Give the direction as an angle below the negative x-axis.
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Textbook Question
A position vector in the first quadrant has an x-component of 6 m and a magnitude of 10 m. What is the value of its y-component?
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