Consider the following planes. 3x + 6y - z = 84 x - 12y + 2z = 0 (a) Find the angle between the two planes. (Round your answer to two decimal places.) (b) Find a set of parametric equations for the line of intersection of the planes. (Use t for the parameter. Enter your answers as a comma-separated list of equations.)

Q: Consider the following planes. 3x + 2y - z = 42 x - 4y + 2z = 0 (a) Find the angle between the two…

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Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

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Q: In the given equation as  follws , find a set of parametric equations forthe rectangular equation…

A: Given :                 y = 2x -5 , t=0 at point (3,1)

Q: oblem 20. Does the line with parametric equation x = 21 + 1, y = 3t- 2, z = 2t – 2, 1 e R intersect…

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Q: b) Given two planes 71 : 2x – 4y + z = 5 and T2 : 7x + y – 2z = 14. i. Find the acute angle between…

A: We will find the angle and the equation of line as following.

Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 42² = 4…

A: To find: Parametric equation of the Intersections of the curves  4x2+y2+4z2=4 and y2=x2+2z2.

Q: Complete the parametric equations for the line where the planes – 3x – 9y – 12z - 11x + 2y – 10z 33…

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Q: Consider the following planes. 3x + 2y - z = 28 x - 4y + 2z = 0 (a) Find the angle between the two…

A: The givne planes are 3x+2y-z=28 .......................... (1)…

Q: Find parametric equations for the line segment joining the points (5, 3) and (11, 11). x=t, y = 3 +…

A: Solution

Q: 1: Find the angle between the planes 3x - 6y + 4z 3 and 2x - 2y +z = 4 then find the parametric…

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Q: Sketch the plane curve represented by the parametric equations x = Vi and y = 2t – 1 by eliminating…

A: Sketch the plane curve represented by the parametric equations             x=t     and     y=2t-1 by…

Q: Find the angle between the two planes 3x + 2y − z = 7,  x − 4y + 2z = 0 and find a set of parametric…

A: Known fact: The angle between two planes a1x+b1y+c1z+d1=0  and a2x+b2y+c2z+d2=0 is given by…

Q: Consider the following planes. −2x + y + z = 2 6x − 3y + 2z = 4 (a) Find the angle…

A: Consider the following planes. −2x + y + z   =   2 6x − 3y + 2z   =   4

Q: Consider the following planes. -2x + y + z = 2 10x – 5y + 2z = 4 (a) Find the angle between the two…

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Q: Consider the following planes. 3x + 6y-z = 126 x 12y + 2z = 0 (a) Find the angle between the two…

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Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is per- pendicular to…

A: Let's find.

Q: Consider the following planes. 3x + 6y – z = 126 x - 12y + 2z = 0 (a) Find the angle between the two…

A:

Q: Find the parametric equations of the line of intersection of the planes, and find the angle between…

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Q: Find the parametric equations for the line in which the planes x-2y+4z=2 and x+2y-2z=6 intersects

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Q: Without eliminating the parameter t, find a Cartesian equation for the lin curve C, defined by the…

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Q: Consider the following planes. 5x + 6y – z = 66 x - 12y + 2z = 0 (a) Find the angle between the two…

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Q: Select the following sets of parametric equations that describe the parabola y = x² x=t, y=t² □ y =…

A: To select the follwing sets of parametric equations that describe the parabola y=x2.1 x=t, y=t22…

Q: Sketch and describe the orientation of the curve given by the parametric equations. x = V7, y = 2t –…

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Q: Consider the following planes. 3x + 4y - z = 56 x - 8y + 2z = 0 (a) Find the angle between the two…

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Q: Consider the following planes. 3x + 6y - z = 84 x - 12y + 2z = 0 (a) Find the angle between the two…

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Q: Consider the following planes. -5x + y + z = 5 15x - 3y + 5z = 25 (a) Find the angle between the two…

A: Let's find.

Q: Consider the following planes. 3x + 4y - z = 28 x - 8y + 2z =0 (a) Find the angle between the two…

A: In this question we have to find the angle between two planes and set of parametric equations.

Q: Consider the following planes. -4x + y + z = 4 12x - 3y + 4z = 16 (a) Find the angle between the two…

A: given planes are, -4x+y+z=4 12x-3y+4z=16

Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Find the parametric equation for the line where the planes 4x – by + 8z = - 36 and – by + z = – 15…

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Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: Try to sketch by hand the curve of intersection of the circu- lar cylinder x + y² = 4 and the…

A: Given, Circular cylinder, x2+y2=4 Parabolic cylinder, z=x2

Q: Consider the following planes. -5x + y + z = 5 20x - 4y + 5z = 25 (a) Find the angle between the two…

A: Consider the following planes -5x+y+z=520x-4y+5z=25a To find the angle between the two planes.b To…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid r² + 4y² -z = 0…

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Q: Find the parametric equations of the line segment through the origin and perpendicular to the plane…

A: Given: Given equation of the plane is x-2y+3z=5 We want to find the parametric equations of the line…

Q: Given the planes 3.x – 6y – 2z = 15 and 2x + y – 2z = 5 anser the following. (b) Find parametric…

A: I have solved using an intersection point and direction ratios

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x –…

A: Cross product of normals of planes is normal to the required line of intersection

Q: Consider the following planes. 3x + 4y - z = 28 x - 8y + 2z = 0 (a) Find the angle between the two…

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Q: Find the parametric equations for the line of intersection of the planes x+y-z = -20 and 9.x + 3y +…

A: Given planes, x+y-z=-20 and 9x+3y+z=16. The objective is to find the parametric equations for the…

Q: Consider the following planes. 3x + 2y - z = 42 X - 4y + 2z = 0 (a) Find the angle between the two…

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Q: 22. Find (a) parametric equations for the line of intersection, and (b) the cosine of the angle…

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Q: Consider the following planes. 5x + 2y - z = 44 X - 4y + 2z = 0 (a) Find the angle between the two…

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Q: Find the parametric equation for the line where the planes 4x – 6y + 8z = - 36 and – 6y + z = – 15…

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Q: ler the following planes. -6x + y + z = 6 18x - 3y + 6z = 36 Find the angle between the two planes.…

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Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x -…

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Q: Consider the following planes. -6x + y + z = 6 24x - 4y + 6z = 36 (a) Find the angle between the two…

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Q: Consider the following planes. -6x + y + z = 6 12x – 2y + 6z = 36 (a) Find the angle between the two…

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Q: Consider the following planes. 5x + 6y – z = 132 X - 12y + 2z = 0 (a) Find the angle between the two…

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Q: Consider the following planes. 3x + 2y z = 28 x - 4y + 2z = 0 (a) Find the angle between the two…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.