Chapter 9: Q. 39 (page 630)

A vector v has initial point $P = (1, 3, - 2)$ and terminal point $Q = (4, - 2, 1) .$ Write vin the form $v = a i + b j + c k .$

Short Answer

Expert verified

The vector is $3 i - 5 j + 3 k .$

Step by step solution

Step 1. Given Information

The initial point of vector v is $P = (1, 3, - 2)$ and the terminal point of vector v is $Q = (4, - 2, 1) .$

Step 2. Writing vector v in the form v=ai+bj+ck

To write the vector v, we will use initial and terminal points in the way such as $v = (x_{2} - x_{1}) i + (y_{2} - y_{1}) j + (z_{2} - z_{1}) k$

Here,

$P = (x_{1}, y_{1}, z_{1}) = (1, 3, - 2) Q = (x_{2}, y_{2}, z_{2}) = (4, - 2, 1)$

So,

role="math" localid="1646990954182" $v = (x_{2} - x_{1}) i + (y_{2} - y_{1}) j + (z_{2} - z_{1}) k v = (4 - 1) i + (- 2 - 3) j + (1 + 2) k v = 3 i - 5 j + 3 k$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A vector v has initial point $P = (1, 3, - 2)$ and terminal point $Q = (4, - 2, 1) .$ Write vin the form $v = a i + b j + c k .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Writing vector v in the form v=ai+bj+ck

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Calculus

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

A vector v has initial point P=1,3,-2and terminal point Q=4,-2,1. Write vin the formv=ai+bj+ck.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Writing vector v in the form v=ai+bj+ck

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Calculus

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

A vector v has initial point $P = (1, 3, - 2)$ and terminal point $Q = (4, - 2, 1) .$ Write vin the form $v = a i + b j + c k .$