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Ch. 4 - Laws of Sines and Cosines; Vectors
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Not the one you use?Change textbook
All textbooksBlitzer 3rd EditionCh. 4 - Laws of Sines and Cosines; VectorsProblem 21
Chapter 4, Problem 21

In Exercises 21–38, letu = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find each specified vector or scalar.u + v

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Identify the components of vector \( u \) as \( 2i - 5j \).
Identify the components of vector \( v \) as \( -3i + 7j \).
Add the corresponding components of vectors \( u \) and \( v \): \( (2i + (-3i)) \) and \( (-5j + 7j) \).
Simplify the addition of the \( i \) components: \( 2i - 3i \).
Simplify the addition of the \( j \) components: \( -5j + 7j \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vector Addition

Vector addition involves combining two or more vectors to form a resultant vector. This is done by adding their corresponding components. For example, if vector u has components (2, -5) and vector v has components (-3, 7), their sum is calculated by adding the i-components and the j-components separately, resulting in a new vector.
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Adding Vectors Geometrically

Component Form of Vectors

Vectors can be expressed in component form, typically as a combination of unit vectors i and j in a two-dimensional space. For instance, a vector u = 2i - 5j indicates it has a horizontal component of 2 and a vertical component of -5. Understanding this form is essential for performing operations like addition or subtraction.
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Resultant Vector

The resultant vector is the vector that results from the addition of two or more vectors. It represents the cumulative effect of the individual vectors. In the context of the question, finding u + v will yield a resultant vector that combines the effects of both vectors, providing a new direction and magnitude.
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Related Practice
Textbook Question
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.a = 6.1, b = 4, A = 162°
Textbook Question
In Exercises 22–24, sketch each vector as a position vector and find its magnitude.v = -3i - 4j
Textbook Question
In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 3, b = 9, c = 8
Textbook Question
In Exercises 17–22, find the angle between v and w. Round to the nearest tenth of a degree.v = 6i, w = 5i + 4j
Textbook Question
In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.a = 57.5, c = 49.8, A = 136°
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Textbook Question
In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.a = 3, b = 3, c = 3