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Problem 4.40
In Exercises 39–46, find the unit vector that has the same direction as the vector v.
v = -5j
Problem 4b
In Exercises 1–4, u and v have the same direction. In each exercise: Find ||v||.
Problem 5
In Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = 3i + j
Problem 7
In Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = i - j
Problem 23
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
u - v
Problem 25
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
v - u
Problem 27
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
5v
Problem 29
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
-4w
Problem 31
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
3w + 2v
Problem 33
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
3v - 4w
Problem 35
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
||2u||
Problem 37
In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.
||w - u||
Problem 39
In Exercises 39–46, find the unit vector that has the same direction as the vector v.
v = 6i
Problem 41
In Exercises 39–46, find the unit vector that has the same direction as the vector v.
v = 3i - 4j
Problem 42
In Exercises 39–46, find the unit vector that has the same direction as the vector v.
v = 8i - 6j
Problem 43
In Exercises 39–46, find the unit vector that has the same direction as the vector v.
v = 3i - 2j
Problem 44
In Exercises 39–46, find the unit vector that has the same direction as the vector v.
v = 4i - 2j
Problem 45
In Exercises 39–46, find the unit vector that has the same direction as the vector v. v = i + j
Problem 46
In Exercises 39–46, find the unit vector that has the same direction as the vector v.
v = i - j
Problem 47
In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 6, θ = 30°
Problem 48
Write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given.
||v|| = 8, θ = 45°
Problem 49
In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 12, θ = 225°
Problem 50
Write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given.
||v|| = 10, θ = 330°
Problem 51
In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 1/2, θ = 113°
Problem 55
In Exercises 53–56, let u = -2i + 3j, v = 6i - j, w = -3i. Find each specified vector or scalar. ||u + v||² - ||u - v||²
Problem 61
In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = -10i + 15j
Problem 62
Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.
v = 2i - 8j
Problem 63
In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = (4i - 2j) - (4i - 8j)
Problem 64
Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.
v = (7i - 3j) - (10i - 3j)
Problem 1
In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = 3i + j, w = i + 3j