Homework Help is Here – Start Your Trial Now!
Math
Calculus
If v = 9i - 5j and w = -3i - 4j find v.w. O 59 07 -59 O O -7

If v = 9i - 5j and w = -3i - 4j find v.w. O 59 07 -59 O O -7

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
### Calculating the Dot Product of Two Vectors #### Problem Statement Given vectors: \[ \mathbf{v} = 9\mathbf{i} - 5\mathbf{j} \] \[ \mathbf{w} = -3\mathbf{i} - 4\mathbf{j} \] Find the dot product \(\mathbf{v} \cdot \mathbf{w}\). #### Options - \( 59 \) - \( 7 \) - \( -59 \) - \( -7 \) #### Solution To calculate the dot product of two vectors \(\mathbf{v} = a\mathbf{i} + b\mathbf{j}\) and \(\mathbf{w} = c\mathbf{i} + d\mathbf{j}\), use the formula: \[ \mathbf{v} \cdot \mathbf{w} = ac + bd \] Given: \[ \mathbf{v} = 9\mathbf{i} - 5\mathbf{j} \] \[ \mathbf{w} = -3\mathbf{i} - 4\mathbf{j} \] Plugging in the values: \[ \mathbf{v} \cdot \mathbf{w} = (9)(-3) + (-5)(-4) \] \[ \mathbf{v} \cdot \mathbf{w} = -27 + 20 \] \[ \mathbf{v} \cdot \mathbf{w} = -7 \] Therefore, the correct answer is: - \( -7 \) #### Answer \( -7 \) #### Diagram Explanation There is no diagram or graph provided in the problem. --- **Note:** This type of problem helps in understanding vector operations which are fundamental in physics and engineering. The dot product, in particular, is widely used in projections, work calculations, and determining angles between vectors.
Transcribed Image Text:### Calculating the Dot Product of Two Vectors #### Problem Statement Given vectors: \[ \mathbf{v} = 9\mathbf{i} - 5\mathbf{j} \] \[ \mathbf{w} = -3\mathbf{i} - 4\mathbf{j} \] Find the dot product \(\mathbf{v} \cdot \mathbf{w}\). #### Options - \( 59 \) - \( 7 \) - \( -59 \) - \( -7 \) #### Solution To calculate the dot product of two vectors \(\mathbf{v} = a\mathbf{i} + b\mathbf{j}\) and \(\mathbf{w} = c\mathbf{i} + d\mathbf{j}\), use the formula: \[ \mathbf{v} \cdot \mathbf{w} = ac + bd \] Given: \[ \mathbf{v} = 9\mathbf{i} - 5\mathbf{j} \] \[ \mathbf{w} = -3\mathbf{i} - 4\mathbf{j} \] Plugging in the values: \[ \mathbf{v} \cdot \mathbf{w} = (9)(-3) + (-5)(-4) \] \[ \mathbf{v} \cdot \mathbf{w} = -27 + 20 \] \[ \mathbf{v} \cdot \mathbf{w} = -7 \] Therefore, the correct answer is: - \( -7 \) #### Answer \( -7 \) #### Diagram Explanation There is no diagram or graph provided in the problem. --- **Note:** This type of problem helps in understanding vector operations which are fundamental in physics and engineering. The dot product, in particular, is widely used in projections, work calculations, and determining angles between vectors.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS