Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

8. Vectors

Geometric Vectors

Trigonometry

8. Vectors

Geometric Vectors

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1:22 minutes

Problem 21

Textbook Question

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

Verified step by step guidance

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.

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.

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.