Find parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line, P(x Yo, Z), and a vector n = (a, b, c) that is parallel to the line. Then the equation of the line is x - xo = at, y - Yo = bt, z - zo = ct.) x2 - 9xyz + y + 72 = 0, P(1, 1, 1)

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 parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line, P(x Yo z), and a vector
n = (a, b, c) that is parallel to the line. Then the equation of the line is x - xo = at, y - Yo = bt, z - zo = ct.)
x2 - 9xyz + y + 7z = 0, P(1, 1, 1)
Transcribed Image Text:Find parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line, P(x Yo z), and a vector n = (a, b, c) that is parallel to the line. Then the equation of the line is x - xo = at, y - Yo = bt, z - zo = ct.) x2 - 9xyz + y + 7z = 0, P(1, 1, 1)
Expert Solution
Step 1

Let fx,y,z=x2-9xyz+y2+7z2. and given point is P1,1,1.

Partially Differentiating f with respect to x,y and z respectively, we get

                            fx=xx2-9xyz+y2+7z2=2x-9yz

                         fy=yx2-9xyz+y2+7z2=-9xz+2y and 

                       fz=zx2-9xyz+y2+7z2=-9xzy+14z

Therefore at P1,1,1, that is when x=1,y=1,z=1, we have

                    fx=2x-9yz=21-911=-7fy=-9xz+2y=-911+21=-7fz=-9xy+14z=-911+141=7

steps

Step by step

Solved in 2 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, advanced-math and related others by exploring similar questions and additional content below.
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,