Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4 and the plane y=x_ at the point (1,1,√3)
Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4 and the plane y=x_ at the point (1,1,√3)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4 and the plane_y=x_at
the point (1,1,√3)
Expert Solution
Step 1
The parametric form of the tangent line is
where, (a,b,c) is the direction vector and is the point of tangent line.
Let us consider the curve
To determine the tangent line at P is obtained as
- Take two variables in the form of one variable and determine the implicit derivative at P
- The implicit derivatives will be the direction vector of the tangent line '
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
