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)
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
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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 . and given point is .
Partially Differentiating with respect to and respectively, we get
and
Therefore at , that is when , we have
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