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

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

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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)
Transcribed Image Text: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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