27-30 - Equations of Lines A description of a line is given.Find parametric equations for the line.27. The line crosses the z-axis where z = 4 and crosses thexy-plane where x = 2 and y = 5.28. The line crosses the x-axis where x = -2 and crosses thez-axis where z = 10.29. The line perpendicular to the xz-plane that contains the point(2, –1, 5).30. The line parallel to the y-axis that crosses the xz-plane wherex = -3 and z = 2.

As the line crosses z axis thus the x and y axis is 0 thus the vector of plane is P→=(0,0,4). On the…

Answered: 27-30 - Equations of Lines A…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.6: Equations Of Lines And Planes

Problem 29E

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Epicycloid If the circle C of Exercise 63 rolls on the outside of the larger circle, the curve traced out by P is called an epicycloid. Find parametric equations for the epicycloid. Hypocycloid A circle C of radius b rolls on the inside of a larger circle of radius a centered at the origin. Let P be a fixed point on the smaller circle, with the initial position at the point (a,0) as shown in the figure. The curve traced out by P is called a hypocycloid. a Show that parametric equations of hypocycloid are x=(ab)cos+bcos(abb) y=(ab)sinbsin(abb) b If a=4b, the hypocycloid is called an asteroid. Show that in this case parametric equations can be reduced to x=acos3y=asin3 Sketch the curve. Eliminate the parameter to obtain an equation for the asteroid in rectangular coordinates.
Find parametric equations for the line. (Use the parameter t.) the line through the origin and the point (2, 5, −1) x(t), y(t), z(t) = Find the symmetric equations. x 5 = y 2 = −z x 2 = y 5 = −z x − 2 = y − 5 = z + 1 x + 2 = y + 5 = z − 1 x 2 = y 5 = z
a) Find the parametric equations for the line in which the planes x-2y+4z=2 and x + 2y - 2z = 6 intersect. b) Find the parametric equations for the line which passes the point P (-1,0,3) and perpendicular to the plane 3x-7y+5z=21
(a) Find parametric equations for the portion of the cylinder x² + y² = 5 that extends between the planes z = 0 and z = 1. (b) Find parametric equations for the portion of the cylinder x² + z² = 4 that extends between the planes y = 1 and y = 3.
a) Find parametric equations for the line. (Use the parameter t.) The line of intersection of the planes x + y + z = 2 and x + z = 0 (x(t), y(t), z(t)) = b) Find the symmetric equations.

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