2. (a) Find parametric equations for the line through the points P(1,1,2) and Q(2, 2, 1). (b) Prove that the parametric equations x = 5+ 3s, y = 5+3s, z = Е —2 — 3s also describe the line that you found in part (a). (c) Is the line described by the symmetric equations z – 2 у — 1 x – 1 = 2 | 3 orthogonal to the line that you found in part (a)? If it is, prove it! If not, explain why not.

Q: B- Find the parametric equations for the line through point (1,0) and parallel to the function f(x,…

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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: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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Q: Suppose parametric equations for the line segment between (1,9) and (0, Sx(t) = a + bt ly(t) = c+ dt…

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Q: The parametric equation of the line through the points (2, –4,1), (2, –4,1) and (0,4, –10) is: A. x…

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Q: Find the parametric equation of the line that passes through point P(2,3,4) and is perpendicular to…

A: To Determine: Find the parametric equation of the line that passes through point P(2,3,4) and is…

Q: 2. Find the parametric equations of the line passing through the point (-1,4, –3) and is parallel to…

A: Given information is as below: r0=(-1,4-3)v=5i-j=(5,-1,0)

Q: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

Q: 1. a) Find parametric equations of the line of intersection of the planes 3x- 2y+z=0 and…

A: Given : equation of a plane, 3x-2y+z=08x+2y+z-11=0

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

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Q: Which of the following is the parametric equation of the line through the point (1,2,3) and parallel…

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Q: 6. Find the projection of v = | -7 onto the -2 line l of R given by the parametric equation l = tủ,…

A:

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: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: What is the parametric equations of line line through the point (1,2,-1)and is perpendicular to the…

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Suppose parametric equations for the line segment between (1, - 5) and (2, – 6) have the form: Sz(t)…

A: Given xt=a+btyt=c+dt if curve starts at (1 , -5) when t=0 and ends at (2 , -6) at t = 1 then we have…

Q: Suppose parametric equations for the line segment between (7, 3) and (3, 0) have the form: S z(t) =…

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Q: The parametric equation of the line through the origin that is parallel to the line given by x = t,…

A:

Q: Suppose parametric equations for the line segment between (2, a(t) 6) and (0, 0) have the form: = a…

A: Explanation of the solution is given below...

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: 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: 2. Find the point(s) of intersection of the following two parametric curves, by first eliminating…

A: From x=t+5 we get t=x-5 Then we plug this in the y=t2 So, the equation is: y=(x-5)2   We can plug…

Q: 2. Find the symmetric and parametric equations of the line containing the point A(1,2, 1) and x-2…

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4…

A: This is the problem from the vector algebra and 3D geometry.

Q: Suppose parametric equations for the line segment between (0,-10) and (8,-1) have the form: a + bt…

A:

Q: -10 -8 -6 -4 -2 6 8 10 -10+ Which set of parametric equations represents the curve shown in the…

A: According to the graph , we have

Q: 1. Find the parameter λ in the parametric form of the line l z+2 6:2-3-9-1-2-20 l: = X y so that…

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Q: Suppose parametric equations for the line segment between (3, – 4) and (0, 3) have the form: S ¤(t)…

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Q: The parametric equation for the line passing through P(1,1,5) and parallel to n=(0,0,1) is defined…

A: Topic = Vector

Q: Question 2. (a) Prove that the lines with parametric equations: x = 1+t, y =1+ 6t, z = 2t and x = 1+…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find a parametric equation for the line through the point (2,3, – 1) and perpendicular to the plane…

A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

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

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Q: Which of the following is Parametric equations for the line passing through the origin and A(1, 0,…

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Q: Find an equation of the line through (0,0,0) that is parallel to the e parametric equations x(t) = 2…

A: To find out equation of any line we need one point on the line and a vector which is parallel to the…

Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) =…

A: This is the answer of question no. 4.

Q: Which of the following is Parametric equations for the line passing through the origin and A(3, -2,…

A: We will use Standard form of parametric equation of Line passing through two points

Q: 1/a- Find the parametric equation of the line passing through Po(1,3,4) parallel to 21-j+5k b- Find…

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Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line (x-4) = 2…

A: The solution is given below in the next step:

Q: Suppose parametric equations for the line segment between (0,-10) and (8,-1) have the form: a + bt y…

A:

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: 7. Find the parametric equations of the line passing through A(1, -2, 6) and which is perpendicular…

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Q: Which of the following is the parametric equation of the line through the point (1,2,3) and parallel…

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Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x – 5 between…

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Q: -10 -8 -6 -4 4 6 8 10 -10- Which of the following sets of parametric equations correctly represents…

A: Given: The curve as To determine: Parametric equation of given curve.

Q: 2. Find the parametric equations of the line through (0, 3) that is parallel to the line x= -5 + t y…

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Q: Suppose parametric equations for the line segment between (3, 1) and (2, 4) have the form: ( x(t) =…

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Q: Suppose parametric equations for the line segment between (-2,-5) and (0, - 5) have the form: [ r(t)…

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y² = 8 ,…

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Q: Suppose parametric equations for the line segment between (6, 1) and (7, 7) have the form: Sx(t) = a…

A: We have find four unknowns so we need four independent equations.

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.