COPY EDIT NOTE: THIS SHOULD NOT BE A PARTS QUESTION. Find each of the following. a = <3, -4> b = <-5, 2> (a) a + b < -2 (b) 4a + 5b -13 (c) | a | 5 (d) | a - b | 68 X I -2 -6

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...
icon
Related questions
Question

How do you find the absolute values of the vectors a-b.

Here's a transcription and explanation suitable for an educational website:

---

**Vectors and Their Operations**

**Copy Edit Note:** This should not be a parts question.

**Task:** Find each of the following for the given vectors.

Vectors:
\[ \mathbf{a} = \langle 3, -4 \rangle \]
\[ \mathbf{b} = \langle -5, 2 \rangle \]

**(a) Vector Addition (\(\mathbf{a} + \mathbf{b}\))**

Calculate \(\mathbf{a} + \mathbf{b}\):
\[ \langle 3, -4 \rangle + \langle -5, 2 \rangle = \langle -2, -2 \rangle \]

Result: \(\langle -2, -2 \rangle\) ✔

**(b) Linear Combination (\(4\mathbf{a} + 5\mathbf{b}\))**

Calculate \(4\mathbf{a} + 5\mathbf{b}\):
\[ 4 \times \langle 3, -4 \rangle + 5 \times \langle -5, 2 \rangle = \langle 12, -16 \rangle + \langle -25, 10 \rangle = \langle -13, -6 \rangle \]

Result: \(\langle -13, -6 \rangle\) ✔

**(c) Magnitude of \(\mathbf{a}\) (\(|\mathbf{a}|\))**

Calculate \(|\mathbf{a}|\):
\[ |\mathbf{a}| = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

Result: \(5\) ✔

**(d) Magnitude of the Difference (\(|\mathbf{a} - \mathbf{b}|\))**

Calculate \(\mathbf{a} - \mathbf{b}\):
\[ \mathbf{a} - \mathbf{b} = \langle 3, -4 \rangle - \langle -5, 2 \rangle = \langle 8, -6 \rangle \]

Calculate \(|\mathbf{a} - \mathbf{b}|\):
\[ |\langle 8, -6
Transcribed Image Text:Here's a transcription and explanation suitable for an educational website: --- **Vectors and Their Operations** **Copy Edit Note:** This should not be a parts question. **Task:** Find each of the following for the given vectors. Vectors: \[ \mathbf{a} = \langle 3, -4 \rangle \] \[ \mathbf{b} = \langle -5, 2 \rangle \] **(a) Vector Addition (\(\mathbf{a} + \mathbf{b}\))** Calculate \(\mathbf{a} + \mathbf{b}\): \[ \langle 3, -4 \rangle + \langle -5, 2 \rangle = \langle -2, -2 \rangle \] Result: \(\langle -2, -2 \rangle\) ✔ **(b) Linear Combination (\(4\mathbf{a} + 5\mathbf{b}\))** Calculate \(4\mathbf{a} + 5\mathbf{b}\): \[ 4 \times \langle 3, -4 \rangle + 5 \times \langle -5, 2 \rangle = \langle 12, -16 \rangle + \langle -25, 10 \rangle = \langle -13, -6 \rangle \] Result: \(\langle -13, -6 \rangle\) ✔ **(c) Magnitude of \(\mathbf{a}\) (\(|\mathbf{a}|\))** Calculate \(|\mathbf{a}|\): \[ |\mathbf{a}| = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] Result: \(5\) ✔ **(d) Magnitude of the Difference (\(|\mathbf{a} - \mathbf{b}|\))** Calculate \(\mathbf{a} - \mathbf{b}\): \[ \mathbf{a} - \mathbf{b} = \langle 3, -4 \rangle - \langle -5, 2 \rangle = \langle 8, -6 \rangle \] Calculate \(|\mathbf{a} - \mathbf{b}|\): \[ |\langle 8, -6
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

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