a. Explanation Given information: the lines are given; r 1 ( t ) = 〈 5 t , 2 t − 1 , 2 t − 2 〉 ; r 2 ( t ) = 〈 t − 5 , − t + 4 , t − 7 〉 Formula Used : x 1 = x 2 ; y 1 = y 2 ; z 1 = z 2 Calculation: If the two lines intersectat the point of intersection their x coordinates , y coordinates and z coordinates are equal. Therefore, r 1 ( t ) = 〈 5 t , 2 t − 1 , 2 t − 2 〉 ; r 2 ( t ) = 〈 t − 5 , − t + 4 , t − 7 〉 So, 5 t = t − 5 or 2 t − 1 = − t + 4 or 2 t − 2 = t − 7 . So, we get three solutions for t b. To determine To Find: whether the lines have a point of intersection . If they do the equation of the plane containing the point of intersection.

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 13.5, Problem 28E

To determine

To Find:whether the lines have a point of intersection. If they do the equation of the plane containing the point of intersection.

To determine

To Find:whether the lines have a point of intersection. If they do the equation of the plane containing the point of intersection.

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Chapter 13.5, Problem 27E

Chapter 13.5, Problem 29E

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In each case, determine whether or not the lines have a single point ofintersection. If they do, give an equation of a plane containing them.(a) r1(t) = (t,2t - l,t -3) andr2(t) = (4,2t -1,-1)(b) r1(t) = (3t,2t+ 1,t-5) andr2(t) = (4t,4t-3,-1)

29. In each case, determine whether or not the point lies on the line. If itdoes not, give an equation of a plane containing the point and the line.(b) (3, -3, 2) and r(t) = (4t + 3, 4t - 3, t + 1) Since (b) is not on the line, how to calculate its equation of plane?

Find an equation of the plane that passes through the point (1,1,2) and contains the line x=3t, y=1, z=2-t

Chapter 13 Solutions

CALCULUS (CLOTH)

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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whether the lines have a point of intersection . If they do the equation of the plane containing the point of intersection.

Solution Summary: The author explains that the lines do not have a single point of intersection if they do the equation of the plane containing the point.

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To Find:whether the lines have a point of intersection. If they do the equation of the plane containing the point of intersection.

To Find:whether the lines have a point of intersection. If they do the equation of the plane containing the point of intersection.

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Chapter 13 Solutions