Let A(2, 1, 1), B(1, 2, 1), and C(1, 1, 2) be three given points. Find (i) parametric and symmetric equations of the line through the point A and parallel to the line through the points B and C;

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

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Q: Find the vector, parametric, and symmetric equations of the line which passes through the points A =…

A: Given points are: A=3,1,-1 and B=7,0,1 To find the vector, parametric, and symmetric equations

Q: 11. Find parametric equations for the line that contains the points P(2, -4, 7) and Q(0, –3, 5).

A: If Px0 ,y0,z0 and Qx1,y1,z1 are any two points then the parametric equation of the line containing…

Q: Find parametric equations for the line that passes through the points P(-3,7,9) and Q(4, 1, -5).

A: The given points are P-3,7,9 and Q4,1,-5. The line containing the point x0,y0,z0 and parallel to the…

Q: 2) Find the parametric and symmetric equations for the line through (1, –1, 1) and parallel to the…

A: Solved below

Q: Q3\Find the parametric and symmetric equations of the line through the points (3,2,0) and (- 5,0,…

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Q: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

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Q: (d) Find the parametric equation for the line segment from point P(1,3, 2) and Q(1, –1,6).

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Q: 29. In each case, determine whether or not the point lies on the line. If it does not, give an…

A: The line passes through the point B=3,-3,1 and has direction vector v→=4,4,1. Another vector in the…

Q: D) Find the parametric and symmetric equations of the line through the points(1, and (-5, 4, 2).

A: Given query is to find the equation of the line.

Q: Find symmetric and parametric equations of the line through the two points (−3, 5, 2) and (1, −3,…

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Q: Example 3: Find the parametric and symmetric equations of the line passing through the point (-3, 5,…

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Q: Find the equation of a plane passing through ?(2,1,3), ?(3, −1,5), and ?(1,2, −3)

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Q: Find parametric equations for the line segment joining the points (-7, 6) and (5, 3). x=-7+12t, y…

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Q: Find the parametric equations of the line segment that passes through the points A(4,2,-5) and…

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Q: Find parametric equations and an equation in vector form for the lines in R2 with the following…

A: Given: y=3x-1 To Find: Parametric Equation and and equation in vector form for the lines in R2 with…

Q: An implicit equation for the plane passing through the points (2,0,−2), (7,−3,−2), and (7,2,3)…

A: Given: A plane is passing through the points 2,0,-2,7,-3,-2,7,2,3. The implicit equation equation…

Q: 1. Write vector and parametric equations of the line. a) parallel to the line x+6y = 1 and through…

A: Parametric and vector equation of line

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

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Q: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

Q: Find the parametric equations and the symmetric equations of the line that passes through the points…

A: Given: A line is passing through the points P-1, 4, 3 and Q8, 10, 5.

Q: Find parametric equations for the line through the points P(-1,-1, 7) and Q(3, -4, -1) O x = 4t - 1,…

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Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

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Q: give the equation of the line in vector form, parametric form and symmetric form. k) The line…

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Q: The parametric equation of a line passing through A(1,1,1) and B(-1,2,0) is

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Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that: y2+z2=1, x=0

Q: Find the parametric and symmetric equations for the lines with the following conditions. (a) Passing…

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Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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Q: Find the parametric equation of the line joining the pointsA(-5,-3,0) and B(7,1,4)

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Q: Given the points P = (2,3,4), Q = (4,–1,5) and R = (-2,5,6) : a. Find a parametric or vector…

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Q: Find parametric equations for the lines in The line through P(-2, 0, 3) and Q(3, 5, -2)

A: To find the parametric equation for PQ

Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: ind an equation of the plane passing through the given points. (3, 1, 12), (1, -3, 18), (2, -2, 16)

A: Given points are (3, 1, 12), (1, -3, 18)  and  (2, -2, 16)

Q: Write vector and parametric equations of the line. a) parallel to the line x+6y = 1 and through the…

A: We know that the line equation of the line that passes through point (ro→), and parallel to vector…

Q: 4- Find parametric and symmetric equations of the line passing through the points (1,- 1,2) and…

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Q: Given the points P = (2,3, 4), Q = (4,–1,5) and R = (-2,5,6) : a. Find a parametric or vector…

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Q: Determine the parametric and symmetric equations for the line through the given points (2, –7,5),…

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Q: 3. Find the parametric equation of the line passing through the point (-1,0, 3) and in the direction…

A: Equation of the line passing through the point (-1,0,3) in the direction N(7,0,-2) is   ( x+1)/ 7 =…

Q: 6) Find parametric equations for the line through P(0, -2,-2) and Q(1,1,0).

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Q: Find the parametric equations for the line passing through points P(2, -3, 1) and Q(4, 1, -4)

A: Given points are  P2,-3,1,Q4,1,-4

Q: Write the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to…

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Q: For each part, find the equation of the plane satisfying the given conditions. a. Containing the…

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

Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

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Q: (a) Find the parametric equations for the line segment that joins P(1, 0, 1) to Q(2, 3, 1).

A: Given, P(1,01), Q(2,3,1)

Q: Parametrize the line segment joining the points P(-3, 2, -3) and Q(1, -1, 4)

A: we have to parametrize the line segment joining the points P(-3,2,-3) and Q(1,-1,4)   as we know…

Q: a) Find the equation of plane passing through the points (1,1,–1), (6, 4, – 5),(- 4,– 2,3)

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find parametric equations of the line through the given points. (a) (2, −3, 1), (4, 2, 5) (b) (−3,…

A: The parametric form of a line passing through two points px1,y1,z1 and Qx2,y2,z2.Fix P-base…