17. Let a be a standard-position vector with terminal point (-2,-4). Let b be a vector with initial point (1, 2) and terminal point (-1, 4). Find the magnitude of vector -3a +b-4i+j.
17. Let a be a standard-position vector with terminal point (-2,-4). Let b be a vector with initial point (1, 2) and terminal point (-1, 4). Find the magnitude of vector -3a +b-4i+j.
Calculus: Early Transcendentals
8th Edition
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
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Please answer the question #17 with details on how to do it. Please make handwriting legible. Thank you.
![## Vectors Problem Set
### Task d
Determine the vectors \(2\mathbf{a}\), \(-\mathbf{b}\), and \(2\mathbf{a} - \mathbf{b}\). Express the vectors in both the component form and by using standard unit vectors.
### Problems
15. Given vectors:
\[
\mathbf{a} = 2\mathbf{i} + \mathbf{j}, \quad \mathbf{b} = \mathbf{i} + 3\mathbf{j}
\]
16. Given vectors:
\[
\mathbf{a} = 2\mathbf{i}, \quad \mathbf{b} = -2\mathbf{i} + 2\mathbf{j}
\]
17. Given:
Let \(\mathbf{a}\) be a standard-position vector with terminal point \((-2, -4)\). Let \(\mathbf{b}\) be a vector with initial point \((1, 2)\) and terminal point \((-1, 4)\). Find the magnitude of vector \(-3\mathbf{a} + \mathbf{b} - 4\mathbf{i} + \mathbf{j}\).
18. Given:
Let \(\mathbf{a}\) be a standard-position vector with terminal point \((2, 5)\). Let \(\mathbf{b}\) be a vector with initial point \((-1, 3)\) and terminal point \((1, 0)\). Find the magnitude of vector \(\mathbf{a} - 3\mathbf{b} + 14\mathbf{i} - 14\mathbf{j}\).
19. Let \(\mathbf{u}\) and \(\mathbf{v}\) be two nonzero vectors that are nonequivalent. Consider the vectors \(\mathbf{a} = 4\mathbf{u} + 5\mathbf{v}\) and \(\mathbf{b} = \mathbf{u} + 2\mathbf{v}\) defined in terms of \(\mathbf{u}\) and \(\mathbf{v}\). Find the scalar \(\lambda\) such that vectors \(\mathbf{a} + \lambda\mathbf{b}\) and \(\mathbf{u} - \mathbf{v}\) are equivalent.
20. Let \(\mathbf{u}\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1296c196-158c-4a2c-9587-82b5996e9fed%2F0b721425-5859-494e-94f4-bc5d935f1578%2Fakartw.jpeg&w=3840&q=75)
Transcribed Image Text:## Vectors Problem Set
### Task d
Determine the vectors \(2\mathbf{a}\), \(-\mathbf{b}\), and \(2\mathbf{a} - \mathbf{b}\). Express the vectors in both the component form and by using standard unit vectors.
### Problems
15. Given vectors:
\[
\mathbf{a} = 2\mathbf{i} + \mathbf{j}, \quad \mathbf{b} = \mathbf{i} + 3\mathbf{j}
\]
16. Given vectors:
\[
\mathbf{a} = 2\mathbf{i}, \quad \mathbf{b} = -2\mathbf{i} + 2\mathbf{j}
\]
17. Given:
Let \(\mathbf{a}\) be a standard-position vector with terminal point \((-2, -4)\). Let \(\mathbf{b}\) be a vector with initial point \((1, 2)\) and terminal point \((-1, 4)\). Find the magnitude of vector \(-3\mathbf{a} + \mathbf{b} - 4\mathbf{i} + \mathbf{j}\).
18. Given:
Let \(\mathbf{a}\) be a standard-position vector with terminal point \((2, 5)\). Let \(\mathbf{b}\) be a vector with initial point \((-1, 3)\) and terminal point \((1, 0)\). Find the magnitude of vector \(\mathbf{a} - 3\mathbf{b} + 14\mathbf{i} - 14\mathbf{j}\).
19. Let \(\mathbf{u}\) and \(\mathbf{v}\) be two nonzero vectors that are nonequivalent. Consider the vectors \(\mathbf{a} = 4\mathbf{u} + 5\mathbf{v}\) and \(\mathbf{b} = \mathbf{u} + 2\mathbf{v}\) defined in terms of \(\mathbf{u}\) and \(\mathbf{v}\). Find the scalar \(\lambda\) such that vectors \(\mathbf{a} + \lambda\mathbf{b}\) and \(\mathbf{u} - \mathbf{v}\) are equivalent.
20. Let \(\mathbf{u}\
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