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...
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![Title: Vector Addition Problem
Let \(\vec{a} = \langle -3, -2, 3 \rangle\) and \(\vec{b} = \langle -3, 5, 2 \rangle\). Find \(3\vec{a} + 3\vec{b}\).
Step-by-Step Solution:
1. Compute \(3\vec{a}\):
\[
3\vec{a} = 3 \cdot \langle -3, -2, 3 \rangle = \langle 3 \cdot (-3), 3 \cdot (-2), 3 \cdot 3 \rangle = \langle -9, -6, 9 \rangle
\]
2. Compute \(3\vec{b}\):
\[
3\vec{b} = 3 \cdot \langle -3, 5, 2 \rangle = \langle 3 \cdot (-3), 3 \cdot 5, 3 \cdot 2 \rangle = \langle -9, 15, 6 \rangle
\]
3. Add \(3\vec{a}\) and \(3\vec{b}\):
\[
3\vec{a} + 3\vec{b} = \langle -9, -6, 9 \rangle + \langle -9, 15, 6 \rangle = \langle -9 + (-9), -6 + 15, 9 + 6 \rangle = \langle -18, 9, 15 \rangle
\]
Therefore, the vector \(3\vec{a} + 3\vec{b}\) is \(\langle -18, 9, 15 \rangle\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55d3466e-6a31-4aff-972b-e33941523058%2F050a4464-1142-42bd-b8e6-708f26d62359%2Fnsgkrs_processed.png&w=3840&q=75)
Transcribed Image Text:Title: Vector Addition Problem
Let \(\vec{a} = \langle -3, -2, 3 \rangle\) and \(\vec{b} = \langle -3, 5, 2 \rangle\). Find \(3\vec{a} + 3\vec{b}\).
Step-by-Step Solution:
1. Compute \(3\vec{a}\):
\[
3\vec{a} = 3 \cdot \langle -3, -2, 3 \rangle = \langle 3 \cdot (-3), 3 \cdot (-2), 3 \cdot 3 \rangle = \langle -9, -6, 9 \rangle
\]
2. Compute \(3\vec{b}\):
\[
3\vec{b} = 3 \cdot \langle -3, 5, 2 \rangle = \langle 3 \cdot (-3), 3 \cdot 5, 3 \cdot 2 \rangle = \langle -9, 15, 6 \rangle
\]
3. Add \(3\vec{a}\) and \(3\vec{b}\):
\[
3\vec{a} + 3\vec{b} = \langle -9, -6, 9 \rangle + \langle -9, 15, 6 \rangle = \langle -9 + (-9), -6 + 15, 9 + 6 \rangle = \langle -18, 9, 15 \rangle
\]
Therefore, the vector \(3\vec{a} + 3\vec{b}\) is \(\langle -18, 9, 15 \rangle\).
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