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Ch. 7 - Applications of Trigonometry and Vectors
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 7 - Applications of Trigonometry and VectorsProblema 30b
Capitolo 8, Problema 30b

Use the figure to find each vector: u - v. Use vector notation as in Example 4.


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Identify the components of vectors \( \mathbf{u} \) and \( \mathbf{v} \) from the figure. Typically, each vector can be expressed in component form as \( \mathbf{u} = \langle u_x, u_y \rangle \) and \( \mathbf{v} = \langle v_x, v_y \rangle \), where \( u_x \) and \( u_y \) are the horizontal and vertical components of \( \mathbf{u} \), and similarly for \( \mathbf{v} \).
Recall that vector subtraction \( \mathbf{u} - \mathbf{v} \) is performed by subtracting the corresponding components of \( \mathbf{v} \) from \( \mathbf{u} \). This means \( \mathbf{u} - \mathbf{v} = \langle u_x - v_x, u_y - v_y \rangle \).
Calculate the horizontal component of \( \mathbf{u} - \mathbf{v} \) by subtracting the horizontal component of \( \mathbf{v} \) from that of \( \mathbf{u} \): \( u_x - v_x \).
Calculate the vertical component of \( \mathbf{u} - \mathbf{v} \) by subtracting the vertical component of \( \mathbf{v} \) from that of \( \mathbf{u} \): \( u_y - v_y \).
Write the resulting vector in component form as \( \mathbf{u} - \mathbf{v} = \langle u_x - v_x, u_y - v_y \rangle \), which is the vector notation requested.

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Vector Subtraction

Vector subtraction involves finding the difference between two vectors by reversing the direction of the vector to be subtracted and then adding it to the first vector. Algebraically, u - v is equivalent to u + (-v), where -v is the vector v with its direction reversed.
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Adding Vectors Geometrically

Vector Notation

Vector notation typically represents vectors as ordered pairs or components, such as u = <x, y>. This notation allows for straightforward algebraic operations like addition and subtraction by working component-wise, which is essential for expressing the result of u - v clearly.
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i & j Notation

Graphical Representation of Vectors

Vectors can be represented graphically as directed line segments with magnitude and direction. Understanding how to visualize vector subtraction on a graph helps in interpreting the problem and verifying the algebraic result by drawing vectors u, v, and u - v accordingly.
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Finding Direction of a Vector Example 1
Pratica correlata
Domanda del libro di testo

Apply the law of sines to the following: a = √5, c = 2√5, A = 30°. What is the value of sin C? What is the measure of C? Based on its angle measures, what kind of triangle is triangle ABC?

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Domanda del libro di testo

Use the figure to find each vector: u - v. Use vector notation as in Example 4.


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Domanda del libro di testo

Solve each triangle. See Examples 2 and 3.


B = 74.8°, a = 8.92 in., c = 6.43 in.

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Domanda del libro di testo

Use the figure to find each vector: - v. Use vector notation as in Example 4.


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Domanda del libro di testo

Use the figure to find each vector: u + v. Use vector notation as in Example 4.


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Domanda del libro di testo

Use the figure to find each vector: - u. Use vector notation as in Example 4.


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