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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1:36 minutes

Problem 25

Textbook Question

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

Verified step by step guidance

Start by identifying the components of vectors \( v \) and \( u \).

Vector \( v \) is given as \(-3i + 7j\).

Vector \( u \) is given as \(2i - 5j\).

To find \( v - u \), subtract the components of \( u \) from the components of \( v \).

Calculate the difference: \((-3i + 7j) - (2i - 5j) = (-3 - 2)i + (7 - (-5))j\).

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Key Concepts

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

Vector Subtraction

Vector subtraction involves finding the difference between two vectors by subtracting their corresponding components. For vectors u = ai + bj and v = ci + dj, the result of v - u is given by (c - a)i + (d - b)j. This operation is essential for determining the relative position or direction between two vectors in a Cartesian plane.

Component Form of Vectors

Vectors in two-dimensional space can be expressed in component form as a combination of unit vectors i and j, where i represents the x-direction and j represents the y-direction. For example, the vector u = 2i - 5j has a horizontal component of 2 and a vertical component of -5. Understanding this representation is crucial for performing vector operations like addition and subtraction.

Resultant Vector

The resultant vector is the vector that results from the addition or subtraction of two or more vectors. In the case of vector subtraction, the resultant vector indicates the direction and magnitude of the difference between the two original vectors. This concept is fundamental in physics and engineering, where understanding the net effect of multiple forces or movements is necessary.