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8-13. Vector-valued functions Find a function r(t) that describes each of the following curves. 8. The line segment from P(2, -3, 0) to Q(1, 4, 9) 9. The line passing through the point P(4, -2, 3) that is orthogonal to the lines R(t) = (t, 5t, 2t) and S(t) = (t + 1, –1, 3t – 1) 10. A circle of radius 3 centered at (2, 1, 0) that lies in the plane y =1 11. An ellipse in the plane x = 2 satisfying the equation 9 =D1 16 12. The projection of the curve onto the xy-plane is the parabola y = x, and the projection of the curve onto the xz-plane is the line z = x. 13. The projection of the curve onto the xy-plane is the unit circle x + y = 1, and the projection of the curve onto the yz-plane is the |3D line segment z = y, for -1

8-13. Vector-valued functions Find a function r(t) that describes each of the following curves. 8. The line segment from P(2, -3, 0) to Q(1, 4, 9) 9. The line passing through the point P(4, -2, 3) that is orthogonal to the lines R(t) = (t, 5t, 2t) and S(t) = (t + 1, –1, 3t – 1) 10. A circle of radius 3 centered at (2, 1, 0) that lies in the plane y =1 11. An ellipse in the plane x = 2 satisfying the equation 9 =D1 16 12. The projection of the curve onto the xy-plane is the parabola y = x, and the projection of the curve onto the xz-plane is the line z = x. 13. The projection of the curve onto the xy-plane is the unit circle x + y = 1, and the projection of the curve onto the yz-plane is the |3D line segment z = y, for -1

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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#11, i know the answer r(t)= I don’t know the steps to get there
f. The position vector and the principal unit normal are always parallel on a smooth curve. 2. Sets of points Describe the set of points satisfying the equations x2 + z? = 1 and y = 2. T3-6. Graphing curves Sketch the curves described by the following functions, indicating the orientation of the curve. Use analysis and describe the shape of the curve before using a graphing utility. (2t + 1) i+tj (cos t, 1+ cos? t), for 0 <t < T/2 3. r(t) 4. г(t) 5. r(t) = 4 cos ti+j+4 sin t k, for 0 < t < 2n 6. r(t) = e' i+ 2e' j+ k, for t > 0 7. Intersection curve A sphere S and a plane P intersect along the curve r(t) = sin ti+ v2 cos t j +sin t k, for 0<t< 2n. Find %3D equations for S and P and describe the curve r. 8-13. Vector-valued functions Find a function r(t) that describes each of the following curves. 8. The line segment from P(2, -3, 0) to Q(1, 4, 9) 9. The line passing through the point P(4, –2, 3) that is orthogonal to the lines R(t) = (t, 5t, 2t) and S(t) = (t + 1, – 1, 3t – 1) 10. A circle of radius 3 centered at (2, 1, 0) that lies in the plane y = 1 11. An ellipse in the plane x = 2 satisfying the equation 9. =D1 16 12. The projection of the curve onto the xy-plane is the parabola y = x, and the projection of the curve onto the xz-plane is the line z = x. 13. The projection of the curve onto the xy-plane is the unit circle a? + y line segment z = y, for -1 <y <1. 1, and the projection of the curve onto the yz-plane is the 14-15. Intersection curve Find the curve r(t) where the following surfaces intersect. 14. z= x² – 5y; z = 10x² + 4y – 36 15. x2 + 7y? + 2z? = 9; z= y
Transcribed Image Text:f. The position vector and the principal unit normal are always parallel on a smooth curve. 2. Sets of points Describe the set of points satisfying the equations x2 + z? = 1 and y = 2. T3-6. Graphing curves Sketch the curves described by the following functions, indicating the orientation of the curve. Use analysis and describe the shape of the curve before using a graphing utility. (2t + 1) i+tj (cos t, 1+ cos? t), for 0 <t < T/2 3. r(t) 4. г(t) 5. r(t) = 4 cos ti+j+4 sin t k, for 0 < t < 2n 6. r(t) = e' i+ 2e' j+ k, for t > 0 7. Intersection curve A sphere S and a plane P intersect along the curve r(t) = sin ti+ v2 cos t j +sin t k, for 0<t< 2n. Find %3D equations for S and P and describe the curve r. 8-13. Vector-valued functions Find a function r(t) that describes each of the following curves. 8. The line segment from P(2, -3, 0) to Q(1, 4, 9) 9. The line passing through the point P(4, –2, 3) that is orthogonal to the lines R(t) = (t, 5t, 2t) and S(t) = (t + 1, – 1, 3t – 1) 10. A circle of radius 3 centered at (2, 1, 0) that lies in the plane y = 1 11. An ellipse in the plane x = 2 satisfying the equation 9. =D1 16 12. The projection of the curve onto the xy-plane is the parabola y = x, and the projection of the curve onto the xz-plane is the line z = x. 13. The projection of the curve onto the xy-plane is the unit circle a? + y line segment z = y, for -1 <y <1. 1, and the projection of the curve onto the yz-plane is the 14-15. Intersection curve Find the curve r(t) where the following surfaces intersect. 14. z= x² – 5y; z = 10x² + 4y – 36 15. x2 + 7y? + 2z? = 9; z= y
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