Open Question
In Exercises 1–4, u and v have the same direction. In each exercise:Find ||v||.
8. Vectors
Geometric Vectors
Back8. Vectors
Geometric Vectors
- Open QuestionIf P₁ = (-2, 3), P₂ = (-1, 5), and v is the vector from P₁ to P₂,Write v in terms of i and j.
- Open QuestionIn Exercises 5–12, sketch each vector as a position vector and find its magnitude.v = 3i + j
- Open QuestionIn Exercises 5–12, sketch each vector as a position vector and find its magnitude.v = i - j
- Open Question
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
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- Open Question
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
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- Open Question
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
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- Open Question
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
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- Open Question
Find the angle between the vectors. Round to the nearest tenth of a degree. If the vectors are orthogonal, say so.
〈5, -3〉, 〈3, 5〉
- Open Question
Solve each problem. See Examples 5 and 6.
Distance and Direction of a Motorboat A motorboat sets out in the direction N 80° 00′ E. The speed of the boat in still water is 20.0 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat.
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- Open QuestionIn Exercises 5–12, sketch each vector as a position vector and find its magnitude.v = -6i - 2j
- Open QuestionIn Exercises 5–12, sketch each vector as a position vector and find its magnitude.v = -4i
- Open QuestionIn Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.P₁ = (-4, -4), P₂ = (6, 2)
- Open QuestionIn Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.P₁ = (-8, 6), P₂ = (-2, 3)
- Open QuestionIn Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.P₁ = (-1, 7), P₂ = (-7, -7)