Given m = 6, n = 1, and v = (-4, 7), what is v(n-m)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 7E
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**Question:**

Given \( m = 6, n = 1, \) and \( \mathbf{v} = \langle -4, 7 \rangle \), what is \( \mathbf{v}(n - m) \)?

**Explanation:**

We are asked to find the vector \(\mathbf{v}\) scaled by the difference \(n - m\).

1. First, compute \(n - m\):
   \[ n - m = 1 - 6 = -5 \]

2. Now, scale the vector \(\mathbf{v}\) by \(-5\):
   \[ \mathbf{v}(n - m) = \mathbf{v}(-5) = \langle -4, 7 \rangle \times -5 \]

3. Distribute \(-5\) to each component of the vector:
   \[ \mathbf{v}(n - m) = \langle -4 \times -5, 7 \times -5 \rangle \]
   \[ \mathbf{v}(n - m) = \langle 20, -35 \rangle \]

So, \( \mathbf{v}(n - m) = \langle 20, -35 \rangle \).
Transcribed Image Text:**Question:** Given \( m = 6, n = 1, \) and \( \mathbf{v} = \langle -4, 7 \rangle \), what is \( \mathbf{v}(n - m) \)? **Explanation:** We are asked to find the vector \(\mathbf{v}\) scaled by the difference \(n - m\). 1. First, compute \(n - m\): \[ n - m = 1 - 6 = -5 \] 2. Now, scale the vector \(\mathbf{v}\) by \(-5\): \[ \mathbf{v}(n - m) = \mathbf{v}(-5) = \langle -4, 7 \rangle \times -5 \] 3. Distribute \(-5\) to each component of the vector: \[ \mathbf{v}(n - m) = \langle -4 \times -5, 7 \times -5 \rangle \] \[ \mathbf{v}(n - m) = \langle 20, -35 \rangle \] So, \( \mathbf{v}(n - m) = \langle 20, -35 \rangle \).
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