you represent this relationship mathematically? gent vector v at (xo Yos Zo)? How 2. Consider a point (xos yo 2o) on a surface given by F(x, y, z) = 0. What is the relationship between VF(xo, Yo, Zo) and the normal line through (xo. Yo Zo)? Describing a Surface In Exercises 3-6, describe the surface F(x, y, z) = 0. 3. F(x, y, z) = 3x 5y + 3z - 15 4. F(x, y, z) = 36 - x² - y² - z² 5. F(x, y, z) = 4x² +9y² - 4z² 6. F(x, y, z) 16x²9y2 + 36z TEE asdi: Finding a Unit Normal Vector In Exercises 7 an a unit normal vector to the surface at the given poi Normalize the gradient vector VF(x, y, z).] Point (0, 0, 0) (-1,1,-1) Surface out 7. 3x + 4y + 12z = 0 8. x²y³ - y²z + 2xz³ = 4 Finding an Equation of a Tangent Plane 9-18, find an equation of the tangent plane to t the given point. ansibe

you represent this relationship mathematically? gent vector v at (xo Yos Zo)? How 2. Consider a point (xos yo 2o) on a surface given by F(x, y, z) = 0. What is the relationship between VF(xo, Yo, Zo) and the normal line through (xo. Yo Zo)? Describing a Surface In Exercises 3-6, describe the surface F(x, y, z) = 0. 3. F(x, y, z) = 3x 5y + 3z - 15 4. F(x, y, z) = 36 - x² - y² - z² 5. F(x, y, z) = 4x² +9y² - 4z² 6. F(x, y, z) 16x²9y2 + 36z TEE asdi: Finding a Unit Normal Vector In Exercises 7 an a unit normal vector to the surface at the given poi Normalize the gradient vector VF(x, y, z).] Point (0, 0, 0) (-1,1,-1) Surface out 7. 3x + 4y + 12z = 0 8. x²y³ - y²z + 2xz³ = 4 Finding an Equation of a Tangent Plane 9-18, find an equation of the tangent plane to t the given point. ansibe

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.6: Equations Of Lines And Planes

Problem 2E

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Question

Number 7. Find a unit normal vector to the surface at the given point.

What
F(xo, Yo, Zo) and any tangent vector v at (xos Yo Zo)? How
face given by
is the relationship between
do you represent this relationship mathematically?
2. Consider a point (xos yo Zo) on a surface given by
F(x, y, z) = 0. What
VF(xo, Yo, Zo) and the normal line through (xo Yo Zo)?
is the relationship between
Describing a Surface In Exercises 3-6, describe the
surface F(x, y, z) = 0.
3. F(x, y, z) = 3x - 5y + 3z - 15
4. F(x, y, z) = 36 - x² - y² - 2²
4x² + 9y² − 4z²
5. F(x, y, z) =
6. F(x, y, z) =
16x² - 9y² + 36z
Finding a Unit Normal Vector
Exercises 7 a
a unit normal vector to the surface at the given poi
Normalize the gradient vector VF(x, y, z).]
Point
(0, 0, 0)
(-1, 1, -1)
bilpnut sit
Surface
7. 3x + 4y + 12z = 0
8. x²y³ - y²z + 2xz³ = 4
Vector In Ex
Finding an Equation of a Tangent Plane
9-18, find an equation of the tangent plane to t
the given point. ansibegon
019
9. z = x² + y² +3
10. f(x, y) = 2
X

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution