Homework Help is Here – Start Your Trial Now!
Math
Calculus
We denote by ->EF the vector that goes from a point E to a point F. Consider A = (3, -1, 5), B= (1, 3, 7) and C= (2, 2, 2). Find a non-zero vector orthogonal to ->CA and another one parallel to it

We denote by ->EF the vector that goes from a point E to a point F. Consider A = (3, -1, 5), B= (1, 3, 7) and C= (2, 2, 2). Find a non-zero vector orthogonal to ->CA and another one parallel to it

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
We denote by ->EF the vector that goes from a point E to a point F. Consider A = (3, -1, 5), B= (1, 3, 7) and C= (2, 2, 2). Find a non-zero vector orthogonal to ->CA and another one parallel to it
Transcribed Image Text:We denote by ->EF the vector that goes from a point E to a point F. Consider A = (3, -1, 5), B= (1, 3, 7) and C= (2, 2, 2). Find a non-zero vector orthogonal to ->CA and another one parallel to it
Expert Solution
Step 1

given:

A=(3,-1,5)

B=(1,3,7)

C=(2,2,2)

Step 2

the non zero orthogonal vetor to CA can be find out by making the dot product of the two vectors equal to zero.

let the non zero orthogonal vector be b.

and b=xi+yj+zk

therefore the dot product of CA and b is zero.

the vector CA is:

CA→=(3-2)i+(-1-2)j+(5-2)k=i-3j+3k

therefore the dot product of the vector b and CA is zero.

therefore,

x-3y+3z=0

Step 3

let y=1 and z=2

calculate the value of x.

x-3(1)+3(2)=0x-3+6=0x+3=0x=-3

therefore the  vector b is -3i+j+2k.

therefore the vector orthogonal to CA vector is -3i+j+2k.

 

steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Cartesian Coordinates
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS