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Determine whether the lines intersect, and if so, find the point of intersection and the cosine of the angle of intersection. 5--2+1, - y + 2 - - z + 1, 4 -3 Part 1 of 6 The symmetric equations are given. Write these equations in parametric form. first equation: x = 3t, y = 2 2 - t, z = -1 -1 +t second equation: x - 1 + 4s, y = -2 + s, z = -3 3s Part 2 of 6 You have found the parametric form of the equations. first equation: x = 3t, y = 2 - t, z - -1 +t second equation: x = 1 + 4s, y = -2 + s, z = -3 - 3s The two lines intersect each other if they have a common point. Let the common point be (x, Y, z). If the common point exists then the parametric equations for each variable are equal at that point. 3t - 1+ 4 4 s, 2 - t - -2 -2 + s, and -1 +t = -3 3s. Part 3 of 6 Now, consider the second of the equations at the possible intersection point and solve for t. 2 -t - -2 +s 7 4 - Part 4 of 6 Substitute t = 4 - s into the first equation 3t = 1 + 4s and solve for s. - s) - 1 + 4s 3( 4

Determine whether the lines intersect, and if so, find the point of intersection and the cosine of the angle of intersection. 5--2+1, - y + 2 - - z + 1, 4 -3 Part 1 of 6 The symmetric equations are given. Write these equations in parametric form. first equation: x = 3t, y = 2 2 - t, z = -1 -1 +t second equation: x - 1 + 4s, y = -2 + s, z = -3 3s Part 2 of 6 You have found the parametric form of the equations. first equation: x = 3t, y = 2 - t, z - -1 +t second equation: x = 1 + 4s, y = -2 + s, z = -3 - 3s The two lines intersect each other if they have a common point. Let the common point be (x, Y, z). If the common point exists then the parametric equations for each variable are equal at that point. 3t - 1+ 4 4 s, 2 - t - -2 -2 + s, and -1 +t = -3 3s. Part 3 of 6 Now, consider the second of the equations at the possible intersection point and solve for t. 2 -t - -2 +s 7 4 - Part 4 of 6 Substitute t = 4 - s into the first equation 3t = 1 + 4s and solve for s. - s) - 1 + 4s 3( 4

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.6: Polar Equations Of Conics
Problem 40E
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Determine whether the lines intersect, and if so, find the point of intersection and the cosine of the angle of intersection. - z + 1, 1-y- z + 3 -3 X - = y + 2 = 4 = Z -1 Part 1 of 6 The symmetric equations are given. Write these equations in parametric form. first equation: x = 3t, y = 2 2 - t, z = |-1| -1 +t second equation: x = 1+ 4s, y = -2 -2 + s, z = -3 - 35 Part 2 of 6 You have found the parametric form of the equations. first equation: x = 3t, y = 2 - t, z = -1 + t second equation: x = 1 + 4s, y = -2 + s, z = -3 - 35 The two lines intersect each other if they have a common point. Let the common point be (x, y, z). If the common point exists then the parametric equations for each variable are equal at that point. 3t = 1 + 4 ss, 2 - t = |-2 -2 + s, and -1 + t = -3 3s. Part 3 of 6 Now, consider the second of the equations at the possible intersection point and solve for t. 2 -t = -2 + s t = 7 4 - Part 4 of 6 Substitute t = 4 - s into the first equation 3t = 1 + 4s and solve for s. 3( 4 s) = 1 + 4s Enter a fraction, integer, or exact decimal. Do not approximate.
Transcribed Image Text:Determine whether the lines intersect, and if so, find the point of intersection and the cosine of the angle of intersection. - z + 1, 1-y- z + 3 -3 X - = y + 2 = 4 = Z -1 Part 1 of 6 The symmetric equations are given. Write these equations in parametric form. first equation: x = 3t, y = 2 2 - t, z = |-1| -1 +t second equation: x = 1+ 4s, y = -2 -2 + s, z = -3 - 35 Part 2 of 6 You have found the parametric form of the equations. first equation: x = 3t, y = 2 - t, z = -1 + t second equation: x = 1 + 4s, y = -2 + s, z = -3 - 35 The two lines intersect each other if they have a common point. Let the common point be (x, y, z). If the common point exists then the parametric equations for each variable are equal at that point. 3t = 1 + 4 ss, 2 - t = |-2 -2 + s, and -1 + t = -3 3s. Part 3 of 6 Now, consider the second of the equations at the possible intersection point and solve for t. 2 -t = -2 + s t = 7 4 - Part 4 of 6 Substitute t = 4 - s into the first equation 3t = 1 + 4s and solve for s. 3( 4 s) = 1 + 4s Enter a fraction, integer, or exact decimal. Do not approximate.
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