1. Write an equation for the set of all points 5 units away from the x-axis.2. The coordinates of point P are (2,3, 7). What is the exact distance between point P and the z-axis?3. Write an equation whose graph is the set of all points whose distance from the yz plane is 9.4. Write an equation for the sphere of radius 7 centered at (-6,4,-1).5. Find a functionr(x, y, z) such that the level surface given by r=13 is the graph off(x, y)=x° cos y-y² +20.6. Let g(x,y,z)=6x² +3xz +5. The level surface given by g=8 is the graph of f(x, y). Find f(x,y).7. Plane P contains the point (5,-4,-1) and is orthogonal to the vector i= 31 – 5j+2k. Find an equation whosegraph is P.8. Find the vector that is the projection of v = 2î +3j-4k ontow=-2i + j+3k (express your answer as a vector%3Dresolved into components parallel to the coordinate axes, that is, in the form ai + bj+ck ).9. Write an equation for the plane containing the points P(5,3,-4); Q(2,6,7); and R(8,4,-2).10. Find a unit vector that points in the same direction as v=i-3j-2k (express your answer as a vector resolvedinto components parallel to the coordinate axes, that is, in the form ai + bj + ck ).Part II(Each correct answer is worth 2 credits)

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Answered: The coordinates of point P are (2,3,7).…

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Calculus

The coordinates of point P are (2,3,7). What is the exact distance between point P and the z-axis?

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.2: Points, Lines, And Their Graphs

Problem 45WE

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Question

100%

1. Write an equation for the set of all points 5 units away from the x-axis.
2. The coordinates of point P are (2,3, 7). What is the exact distance between point P and the z-axis?
3. Write an equation whose graph is the set of all points whose distance from the yz plane is 9.
4. Write an equation for the sphere of radius 7 centered at (-6,4,-1).
5. Find a functionr(x, y, z) such that the level surface given by r=13 is the graph of
f(x, y)=x° cos y-y² +20.
6. Let g(x,y,z)=6x² +3xz +5. The level surface given by g=8 is the graph of f(x, y). Find f(x,y).
7. Plane P contains the point (5,-4,-1) and is orthogonal to the vector i= 31 – 5j+2k. Find an equation whose
graph is P.
8. Find the vector that is the projection of v = 2î +3j-4k onto
w=-2i + j+3k (express your answer as a vector
%3D
resolved into components parallel to the coordinate axes, that is, in the form ai + bj+ck ).
9. Write an equation for the plane containing the points P(5,3,-4); Q(2,6,7); and R(8,4,-2).
10. Find a unit vector that points in the same direction as v=i-3j-2k (express your answer as a vector resolved
into components parallel to the coordinate axes, that is, in the form ai + bj + ck ).
Part II
(Each correct answer is worth 2 credits)

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