Question

In Problems $27-32$, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$; that is, find its position vector. $P=(-1,4,-2) ; \quad Q=(6,2,2)$ 

   In Problems $27-32$, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$; that is, find its position vector.
$P=(-1,4,-2) ; \quad Q=(6,2,2)$
Show more…
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Michael Sullivan 4th Edition
Chapter 8, Problem 32 ↓

Instant Answer

verified

Step 1

The initial point $P$ has coordinates $(-1, 4, -2)$ and the terminal point $Q$ has coordinates $(6, 2, 2)$.  Show more…

Show all steps

lock
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
In Problems $27-32$, the vector $\mathbf{v}$ has initial point $P$ and terminal point $Q$. Write $\mathbf{v}$ in the form $a \mathbf{i}+b \mathbf{j}+c \mathbf{k}$; that is, find its position vector. $P=(-1,4,-2) ; \quad Q=(6,2,2)$
Close icon
Play audio
Feedback
Powered by NumerAI
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Component Form of a Vector
Expressing a vector in component form involves representing it as a sum of its contributions along each coordinate axis. This method simplifies calculations and operations, such as addition, subtraction, and finding magnitudes, by breaking down the vector into its individual directional parts.
Position Vector
A position vector in three-dimensional space represents the location of a point relative to the origin. It is typically expressed in terms of i, j, and k, which denote the unit vectors along the x, y, and z axes.
Vector Subtraction
Vector subtraction is used to determine the displacement between two points by subtracting the coordinates of the initial point from those of the terminal point. This operation yields the components of the vector that describes the direction and magnitude from one point to the other.
*

Recommended Videos

-
the-vector-v-initial-position-p-and-the-terminal-point-q-write-v-in-the-form-ai-bj-find-its-position-vector-p-26-q-32

the vector v initial position P and the terminal point Q. Write v in the form ai + bj; find its position vector. P= (-2,6) Q= (3,2)
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade

Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever