20. Find the coordinates of the point where the line with parametric equations x =1-1, y=3+t, z=3-21 intersects, a. the XOZ plane b. the YOZ plane

Q: Find the real number a such that the line of x = 1, y = 2-1, z=3+t, the plane of equation parametric…

A: Given parametric equations are x=t , y=2-t, z=3+t Where t∈ℝ and  Plane is αx+5y+z-10=0

Q: Find parametric equations for the line through (7,4, – 7) perpendicular to the plane 4x + 5y + 4z =…

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Q: Find the angle between the two planes 6x − 3y + z = 5,  −x + y + 5z = 5 and find a set of parametric…

A: We have given the equation of planes; 6x − 3y + z = 5 −x + y + 5z = 5 Hence the normal vectors of…

Q: Consider the planes II : 3z – y+ 2z=1, Il2 : -9z + 3y – 6z = 24 and the line of parametric equations…

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Q: 3. Find a set of parametric equations for the line of the intersection of the planes 3x-3y-7z -4 and…

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Q: Find a parametric equation for the line through the point(1,9,3) and perpendicular to the plwne…

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Q: A parametric equation of the line of the intersection of the planes x - z = 0 and x – y + 2z = 0 is

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Q: Find the parametric equation of x, y, z where : . z2 = x2 + y2 p. 9 = x2 + y² Nhat is the name of…

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Q: Find parametric equations for the intersection of the planes 2x + y − 3z = 0 and x + y = 1

A: Two planes lying in 3-Dimensional plane can intersect each other at any point and that point can lie…

Q: . Consider the plane P : x +y + z = 2 and point A(0,1, 2). A line L has the parametric equations L:…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: a +…

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Q: Find the real number a such that the line of parametric equations x = t, y = 2 – t, z = 3 + t, te R…

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Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1:2x – y…

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Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: Line of intersection

Q: 1. (a) Parametrize the curve of intersection of the sphere a? + y? + 22 22 + 222 = 1, Try your best…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A: Here we have to find the parametric equations of the curve C of intersection of the cylinder S:x2+y2…

Q: Consider the following planes. 5x – 3y + z = 2, 3x + y - 5z = 4 Find parametric equations for the…

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Q: Given the planes  π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Let L be the line of…

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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 three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

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Q: TRUE OR FALSE. A plane curve C defined by the parametric equations x = f(t) and y = g(t), where t is…

A: check the given statement is true or not.

Q: Determine the parametric equations of the curve of intersection of the paraboloid x? – y? + z² = 0…

A: Detailed explanation mentioned below

Q: Find a parameterization of the line formed by the intersection of the following planes: 1:2x-y+3z 1…

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Q: What are the parametric equations for the intersection of the planes x - y - z = 1 and 2x + 3y + z…

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Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: Find the general equation of the plane through the point (1, 1, 1) that is perpendicular to the line…

A: We know that equation of plane which passes through pointx1,y1,z1 and perpendicular to linex=x2+at,…

Q: For planes 2x+ y – z = 2 and 2x + 3y + 5z = 4. %3D Write the parametric equations of the line at…

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Q: 18. Find the acute angle between the plane x+2y-z=8 and the line with parametric equations x =1, y…

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Q: 4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the…

A: As per the question we are given a closed curve Γ , defined as the intersection of the plane x+y+z =…

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 equation of the line of intersection of two planes correctly: P1:x+3y+5z=0 and…

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Q: (s) (a) Find a parametric equation for the line through (2, 4, 6) that is perpendic- ular to the…

A: Equation of line in 3D

Q: Find the angle between the two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2 and find a set of…

A: Given, two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2  we have to find the angle between the two…

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: Which of the following are parametric equations of the line of intersection of the planes x+2 z=3,…

A: We have to check

Q: ). Find a parametric representation for the line of intersection of the following two planes: I - y…

A: We use cross product to find the direct vector for the line.

Q: Let P(r, y, z) be the point at which the line with parametric equations x = -t, y=3+2t, z=1-t te R,…

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: Complete the parametric equations for the line wherekche planes 2=0and-2z + 2y + 2z -4 intersect.…

A: The equation of the planes are: P1: 2z = 0 ⇒ z = 0                                  .........1 P2:…

Q: # 2. Let C be the curve that is the intersection of the cylinder x²-2x+4y2 = 0 with the plane z-x…

A: The cylinder x2-2x+4y2=1 and a plane z-x=3. We have to find the parametric equations for the…

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: 2)as per our guideline we have to write one question at a time kindly repost remaining questions

Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: Consider the planes 2x − 3y + z = 6 and −2x + 4y − 3z = 4 Find parametric equations x(t), y(t), z(t)…

A: Given :-  The given planes are : 2x -3y + z = 6-2x + 4y -3z = 4 To Determine :-  The Parametric…

Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: <3, 1, 1> +…

Q: Find the parametric equation of the line of intersection of the planes 2x+y-z=1 and x-2y+3z-9

A: First find cross product take normal vector useformula

Q: Give two parametric representations for the plane curve. 1. y#-4 y + 64 %3D

A: