Find the parametric equations of the line of intersection of the planes, and find the angle between the planes.  Plane 1: x + y + z = 1  Plane 2: x + 2y + 2z = 1

Q: 2. Given point P = (1,2,1) and Q(3,3,0) Find a) the parametric equation of line L, which passes…

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Q: c) Find the parametric equations of the line through the point (1,3,-2) and parallel to the vector V…

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Q: Find the parametric equations of the line that goes through the point P(−2, 0, 5) and is parallel to…

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Q: The parametric equations of four plane curves are given (a) x = t and y = t2 - 4. (b) x = t2 and y =…

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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: If the parametric equations are: x cos-t and y = sin then the Cartesian (rectangular)equation is…

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Q: Find a rectangular equation of the portion of the cycloid given by the parametric equations x = a(θ…

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Q: Part A Find the parametric equations of the line of intersection of the following planes: T1: 5x +…

A: Find the point of parametric equation of the line of intersection, and angle between two planes

Q: (a) Find parametric equations for the intersection of the planes 2x + y−z = 3and x + 2y + z = 3.(b)…

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Q: 14. State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Two planes are given by, π1: x-y+z-2 = 0  and π2: 2x+y+z-4 = 0. The objective is to check whether…

Q: 1. Given the point Q(1,-2,4) and a plane p: 3x + 2y + 6z = 5, find %3D a) The distance from Q to p.…

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Q: Find a set of parametric equations for the line passing through the point (7, 0, 1) that is parallel…

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Q: Exn=9sin+2 and v(r)-8 cost+ 2, eliminate the parameter to write the parametric equations as a…

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Q: State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Let's solve.

Q: Find the parametric equation of the line that passes through P(1, 0, -3) and is parallel to the line…

A: Given: We have to find the parametric equation of the line that passes through the point P(1, 0, -3)…

Q: (c) Find parametric equations of a line through the origin and parallel to the line I =1-t, y = 2, z…

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Q: Eliminate the parameter in the parametric equations x(t) = e³t and y(t) = 3e' to a Cartesian form of…

A: Givenx(t)=e3t    ....(1)y(t)=3et     ....(2)

Q: (a) Find parametric equations for the line through  (4, 5, 4) that is perpendicular to the plane x −…

A: Parametric equation of a line passing through (x1, y1, z1) and perpendicular to the plane ax + by +…

Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

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Q: Find parametric equations for the line through the point, that is parallel to the given plane, and…

A: given point 0,2,2 given plane x+y+z=3 given line x=1+t,y=2-t,z=2t

Q: Question If x(t) = –2t – 3 and y(t) = -8t + 3, eliminate the parameter to write the parametric…

A: Given that:                              x = -2t - 3 Or,                        t=x+3-2…

Q: What Cartesian equation is equivalent to the given parametric equations? {x(t)=4sin(t)…

A: For x=a.cos(t) and y=b.sin(t) the Cartesian equation is written as: xa2+yb2=cos2t+sin2t=1.

Q: State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: Given: The equation of two planes are: V1 : x − y + z − 2 = 0, V2 : 2x + y + z − 4 = 0

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

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Q: is a plane, find an equation for it. If it is a line, find parametric equations for it, using t as…

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Q: Consider the following 2 planes: ?1: 2? − ? − 4? − 4 = 0                   ?2: 4? − 2? − 3? = 3…

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Q: Q1: Two lines in space {x 1- 2t,y 2 +3t,z =-1+t} and {x = 1+t,y% 3+ 2t,z = -1+3t} find the angle…

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Q: x = 1 + 4t,    y = 3 − t2

A: Here we extract t from the 1st equation then put this into second equation.

Q: Complete the parametric equations of the line through the points (7,3,-5) and (0,6,1) x(t) = 7 - 7t…

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Q: The parametric equations r = 3 - t, y = 2t + 4, 0 <t < 2 describes motion along a certain line…

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Q: Given the following set of parametric equations, find all points of horizontal and vertical…

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Q: Find parametric equations for the set of all points P as shown in the figure such that |OP| = |AB|

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Q: The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations…

A: Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…

Q: 6) Consider the plane P: z+y-2:= 0 in R³ that contains the point P₁(1, 1, 1). Answer the following…

A: As per the question we are given the plane P and a point P1 on it. Now we have to find the…

Q: b) Find the area of the triangle with vertices P, Q, R. c)Write down parametric equations for the…

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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: Find the projection of v = -7 onto the -2 e of R' given by the parametric equation e = tu, [-11

A: Introduction: The formula of projection of the vector v onto the vector u is given by the formula,…

Q: Complete the parametric equations of the line through the point (-3,1,-4) and perpendicular to the…

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Q: If the parametric equations are : x = cos-t and y %3D then the Cartestan (rectangular)equation is…

A: Given, The parametric equations are  x = cost2   and   y = sint2 -π≤t≤π We have to find the…

Q: Find the parametric equations for the line of intersection of the planes x+y+z= 3 and 2:z-3y = 6.…

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Q: Q5) Find the angle between the plane x+y-z=3 and the plane that perpendicular to the line has the…

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Q: Use the result, “the set of parametric equations for the circle is x-h+rcos & y-k+rsin @ to find a…

A: Coordinate Geometry Question

Q: Find the angle of intersection of the plane -2x – 3y – 5z = -4 with the plane 5x + 5y + 4z = -5.…

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Q: 6) Find the following: a) An equation of the plane passing through the points P(2,1, 10, Q(-1, -1,…

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Q: Find parametric equations for the segment joining the given points. (1, 3) and (3, 6) 0 sts1 c(t)…

A: Let p and q be the points (1,3) and (3,6) The parametric equation of the segment joining p and q is…

Q: B. Find the Cartesian equation for the following parametric equations (a) x = e", y = t+1 (b) x =…

A: Here I'm doing first question ( not mentioned any )

Q: Complete the parametric equations of the line through the point (8,6,-2) and perpendicular to the…

A: equation of line passing passing through the point 8,6,-2 and perpendicular to the plane , x-7y-z=-3

Q: What is the rectangular form of the parametric equations? I (t) = t+ 3, y (t) = 2t² – 4, where t is…

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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.