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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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Can you please explain each step of the solution especially the part I circled. Confused on how to get that answer.

9. Find a parametric equation for the line that is orthogonal to the surface
xyz = 2 at the point (1, 1, 2).
Solution.
The normal vector to the surface f(x, y, z) = 2 with f (x, y, z) = xyz is
Vf(7, y, 2) yzi + α2j + xyk.
Thus, the normal vector at (x, y, z) = (1, 1,2) is
i = Vf(1,1, 2) = 2i + 2j + k.
The normal vector n
(2, 2, 1) is a direction vector of the line, so a
parametric equation of the line is
(x, y, z) = (1, 1, 2) + t(2,2, 1),
or
x = 1+ 2t,
y = 1+ 2t,
z = 2+t.

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