Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let x, y € R. Given that the vectors (xi - y, y + x, -yi) and (1 + ix, 0, x - -y) have unit magnitude, then O(x, y) is a point on the ellipse 4x² + 2x² = 1 O(x, y) is a point on the ellipse 4x² + x² = 1 None of the given options is correct (x, y) is a point on the ellipse x² + 2x² = 1 O(x, y) is a point on the circle with center (1, 1) and radius ○ (x, y) is a point on the circle with center (0,0) and radius O(x, y) is a point on the circle with center (0,0) and radius

Let x, y € R. Given that the vectors (xi - y, y + x, -yi) and (1 + ix, 0, x - -y) have unit magnitude, then O(x, y) is a point on the ellipse 4x² + 2x² = 1 O(x, y) is a point on the ellipse 4x² + x² = 1 None of the given options is correct (x, y) is a point on the ellipse x² + 2x² = 1 O(x, y) is a point on the circle with center (1, 1) and radius ○ (x, y) is a point on the circle with center (0,0) and radius O(x, y) is a point on the circle with center (0,0) and radius

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Let x, y E R. Given that the vectors(xi Y, y + x, –yi) and (1+ ix, 0, x –- y) have unit magnitude, then (x, y) is a point on the ellipse 4x² + 2x² = 1 (x, y) is a point on the ellipse 4x² + x² = 1 None of the given options is correct (x, y) is a point on the ellipse a2 + 2x² = 1 (x, y) is a point on the circle with center (1, 1) and radius ; (x, y) is a point on the circle with center (0, 0) and radius i (x, y) is a point on the circle with center (0,0) and radius ОООО ОО
Transcribed Image Text:Let x, y E R. Given that the vectors(xi Y, y + x, –yi) and (1+ ix, 0, x –- y) have unit magnitude, then (x, y) is a point on the ellipse 4x² + 2x² = 1 (x, y) is a point on the ellipse 4x² + x² = 1 None of the given options is correct (x, y) is a point on the ellipse a2 + 2x² = 1 (x, y) is a point on the circle with center (1, 1) and radius ; (x, y) is a point on the circle with center (0, 0) and radius i (x, y) is a point on the circle with center (0,0) and radius ОООО ОО
Expert Solution
Step 1

let x,y∈ℝ , given that the vectors xi-y , y+x , -yi and 1+ix , 0 , x-y have unit magnitude , then

since xi-y , y+x , -yi is unit vector 

xi-y2+y+x2+-yi2=1

squaring both sides 

xi-y2+y+x2+-yi2=1

simplify the values

x2i2+y2-2ixy+y2+x2+2xy+y2i2=1⇒-x2+y2-2ixy+y2+x2+2xy-y2=1⇒y2+2xy-2ixy=1⇒y2+2xy1-i=1                  ...i

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS