Find the condition for the two lines to be coplanar. a1 + bjx + C7x + d, =0 = az + b2x + C2x + d2 az + b3x + C3x + d3 =0 = a4 + bạx + C4X + d4 I know that the general line passing through the first lines can be represented as a, + b;x + C,x + d, +k(a2 + b2x + C2x + d2), for real number k Also, the general line passing through the second lines can be represented as az + b3x + C3x + dz +d(a4 + bạx + C4x + d4), for real number r How do we then, prove the required result? Thank you!

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Find the condition for the two lines to be coplanar.
a1 + bjx + C7x + d, =0 = az + b2x + C2x + d2
az + b3x + C3x + d3 =0 = a4 + bạx + C4X + d4
I know that the general line passing through the first lines can be represented as a, + b;x + C,x + d,
+k(a2 + b2x + C2x + d2), for real number k
Also, the general line passing through the second lines can be represented as az + b3x + C3x + dz +d(a4
+ bạx + C4x + d4), for real number r
How do we then, prove the required result?
Thank you!
Transcribed Image Text:Find the condition for the two lines to be coplanar. a1 + bjx + C7x + d, =0 = az + b2x + C2x + d2 az + b3x + C3x + d3 =0 = a4 + bạx + C4X + d4 I know that the general line passing through the first lines can be represented as a, + b;x + C,x + d, +k(a2 + b2x + C2x + d2), for real number k Also, the general line passing through the second lines can be represented as az + b3x + C3x + dz +d(a4 + bạx + C4x + d4), for real number r How do we then, prove the required result? Thank you!
Expert Solution
steps

Step by step

Solved in 2 steps

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,