a = < x, y, 1 >b = < 1, -1, 3 >|a| = (14)^(1/2)/2a•b = 5Find all possible values of x and y

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 13E
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a = < x, y, 1 >
b = < 1, -1, 3 >
|a| = (14)^(1/2)/2
a•b = 5
Find all possible values of x and y

Expert Solution
Step 1

As we know dot product and given information

 

Calculus homework question answer, Step 1, Image 1
Step 2

from dot product rule:

Calculus homework question answer, Step 2, Image 1
Step 3

From equation 4 and 5

Calculus homework question answer, Step 3, Image 1
Step 4

 from equation 3 and vector magnitude formula

Calculus homework question answer, Step 4, Image 1
Step 5

From equation 6 and 7 and substitution method

Calculus homework question answer, Step 5, Image 1
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