is a plane, find an equation for it. If it is a line, find parametric equations for it, using t as parameter. 1 -6 1 (c) A 2 -12 2 3 -18 3 The solution space is a plane through the origin Equation: 6x2+ x3 1 -1 1 (d) A = 2 -1 1 15 The solution space is a line through the origin ||

Q: Find parametric equations for the line through (-1,2) and (4, -8). Select all that apply. OA. x =…

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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: Let L denote the intersection of the planes x − y − z = 1 and2x + 3y + z = 2. Find parametric…

A: Given, Two planes x-y-z=1, 2x+3y+z=2 To find the parametric equation for the line L: Let…

Q: 4 The plane t contains the point P(-1,2,–4) and the line 14:r=(2i-5j-3k)+1(-4ị + 2 j+k) (a) Show…

A: Since you have asked multiple subparts, as per our company guidelines we are supposed to answer only…

Q: Q1. The parametric equations of the lines L1, and L2 are given as: L: x=-2+1, y=3+2t, z=-t+4 L₂:…

A: Let's find distance between two lines.

Q: Let Q(3, 1,-6) and let l be the line passing through the point Q and perpendicular to the plane P1…

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Q: Find the solution for the intersection of the following two planes (if it exists). Otherwise show…

A: As per the question we are given two plants as : x - y + 2z = -13 -2x + 2y - 2z = 26 And we have to…

Q: Q1: Find the angle between the planes 3x - 6y + 4z = 3 and 2x 2y + z = 4 then find the parametric…

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Q: 4. Consider the point P(1, -2,5), the plane : 3x + 2y – z = 8, and the line l : x = 5+ 8t, y = 4, z…

A: Plane and line

Q: Find parametric equations for the line through Po = (3, –1, 1) perpendicular to the plane 8x + 5y –…

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Q: Given the following two planes P1 and P2 in R: P : P2: - 7a + 35y + 14z = 28 4x – 19y – 72 = -13 The…

A: Just I have solved and find that , z is free variable , taking z as parameter s and find the…

Q: 4. Consider the lines 4: x=1+3ty=2+3t,z=3-10 and 1₂: a) Find the point of intersection of 1 and 2₂.…

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Q: A communications satellite orbiting the earth has initial posi- tion r = (29,000, 20,000, 0) (in…

A: GIVEN  we need to find the equation of plane containing the satellite 's orbit

Q: Consider the planes π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. (a) Let ? be the line of…

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Q: A)Find the equation of the XZ plane. B)Finde the equation of the plane ,each of whose points is…

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Q: The line L has parametric equations x = 6t – 7, y = –2t – 3, z = t – 3. The line L2 has symmetric…

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Q: 0/ Find the Palametric equations of the line of intersection of Planes? PL= -2x+3y +7Z =-2…

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Q: Let P(1, –2, 4) and v = (3, 1, –5), and let I be the line passing through P and in the direction of…

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Q: Q1) Write the parametric equations of the line of intersection of the planes 2x-y+z 5 Note: Consider…

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

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Q: (i) Find the distance from the point P(-1, 2,1) to the plane II1 : 2x + y – (ii) Find an equation…

A: These problems can be solved by using the standard equations of plane and line in Cartesian form and…

Q: Question 4 2 Let L be the line with the equation -3 +t 2 and let II 4 3 be the plane with equation…

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Q: The parametric equations for a line L7 are as follows: x = 4-6t y = -3-6t z = 2+4t Let L2 be the…

A: Solved below

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: L1 and L2 intersect in a single point. Find that coordinates of that point.  b) Find an equation…

A: In this question, we have three parts. (a) we find the intersection point by taking the general…

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: Line l is given by the parametric equations: x = 1-2t  y = -2+4t z = 4+5t Determine the equation…

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Q: 22 a) Drive the parametric equation of straight line. D) Check whether the following two lines are…

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Q: Find an equation of the plane A through the point P(0,1,−1) and parallel to the plane B −x+ 2y+z=−3…

A: We will find the equation of plane a and the distance between two planes as following

Q: Consider the plane P with equation -2x+y-2z =-6 and line L with equations x =-5-6t y = -5-2t z =…

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

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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: Find the point(s) of intersection (if any) of the plane and the line. Also determine whether the…

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Q: Find parametric equations for the line through Po = (3, -1, 1) perpendicular to the plane 8x + 5y –…

A: Consider the point Po and the equation of the given plane. Find the vector Po and the direction…

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

A: The solution is given as follows

Q: 2. Give the parametric system of equations of the line given by the equations: 2x = 4 – 3y = ±1 Give…

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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: (a) Find parametric equations for the line through (5, 2, 4) that is perpendicular to the plane x -…

A: answer is in next step.

Q: Consider the planes P1: r - 2y +3z +1 =0 and P2: 2x + y + z+2=0. (a) Let l be the line of…

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

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Q: 2) Determine an equation for each of the following planes given the indicated form for each…

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Q: Let L be a line which is parallel to the line L1 : 2x = 3y = 6z and intersects two lines L2 : x = z…

A: For the solution follow the next steps.

Q: Two automobiles are driving on a plane. The first automobile is moving north at 10 m/s and rising 5…

A: Let's consider North as +ve y-axis, East as +ve x-axis, and upward motion to be +ve z-axis. Now, the…

Q: Pr. #1) Find an equation of the plane. Contains the line = = z+ 2 and is orthogonal to the line r =…

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Q: 3. Give the parametric and symmetric equations of the line that passes through the point (2,3,-1)…

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Q: Pr. #2) Find an equation of the plane. Contains the line r+3 = = and is orthogonal to the line r…

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Q: Let P(1,-2, 4) and v = (3, 1,-5), and let l be the line passing through P and in the direction of v.…

A: Introduction: The vector equation of a straight line in three-dimensional geometry is rt=a+tb The…

Q: Find parametric equations for the line described below. The line through the points P(-1, -1, -3)…

A: We have to find parametric form for the line through the points P(-1, -1, -3) and Q(-3, 2, -6)

Q: Q: find the cartesian equation of the plane Containing the point p(2.1.1) and parallel to the plane…

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