Domanda del libro di testo
A plane flies 650 mph on a bearing of 175.3°. A 25-mph wind, from a direction of 266.6°, blows against the plane. Find the resulting bearing of the plane.
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Ch. 7 - Applications of Trigonometry and Vectors
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 8, Problema 53
Find the dot product for each pair of vectors.
4i, 5i - 9j
Guida verificata passo dopo passo1
Identify the given vectors. The first vector is \(\vec{A} = 4\mathbf{i}\) and the second vector is \(\vec{B} = 5\mathbf{i} - 9\mathbf{j}\).
Recall the formula for the dot product of two vectors \(\vec{A} = a_1\mathbf{i} + a_2\mathbf{j}\) and \(\vec{B} = b_1\mathbf{i} + b_2\mathbf{j}\):
\(\vec{A} \cdot \vec{B} = a_1 b_1 + a_2 b_2\).
Extract the components of each vector: For \(\vec{A}\), \(a_1 = 4\) and \(a_2 = 0\) (since there is no \(\mathbf{j}\) component). For \(\vec{B}\), \(b_1 = 5\) and \(b_2 = -9\).
Substitute the components into the dot product formula:
\(\vec{A} \cdot \vec{B} = (4)(5) + (0)(-9)\).
Simplify the expression by multiplying and adding the terms to find the dot product.
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Vector Components and Notation
Vectors are often expressed in terms of unit vectors i, j, and k, representing the x, y, and z directions respectively. Understanding how to identify and separate these components is essential for performing operations like the dot product.
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Percorso guidato
06:01
i & j Notation
Dot Product Definition
The dot product of two vectors is a scalar obtained by multiplying corresponding components and summing the results. For vectors in two dimensions, it is calculated as (x1 * x2) + (y1 * y2), which measures the extent to which the vectors point in the same direction.
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Percorso guidato
05:40Introduction to Dot Product
Properties and Applications of the Dot Product
The dot product is commutative and relates to the angle between vectors through the formula A · B = |A||B|cosθ. It is used to find projections, angles, and to determine orthogonality between vectors.
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Percorso guidato
05:40Introduction to Dot Product
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