What is the parametric equation for the line through the point (1,2,3) parallel to the y- axis? (a) x = 1+ 2t, y = 0, z = 0 (c) x = 0, y = 2 + 3t, z = 0 (b) x = 1+ 5t, y 0, z = 0 (d) a, b, & c

Q: Find parametric equations for the line passing through the points (10,3,1) and (8,6,-2) using the…

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

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Q: 4. Find parametric equations of a line passing through (1, 2, 3) that is parallel to the plane…

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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: Find parametric equations of the line through the point (8, 3, 4) that is parallel to the plane -2x…

A: First find vector normal to plane Write equation of line

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: 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 set of parametric equations of the line through the point (1, 6, 3) that is parallel to the…

A: The direction ratio of the line x=6+5t, y=6+2t, z=4+2t is (5,2,2). Parallel lines have the same…

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: Find the parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

A: The parametric equations for the line in the x-y plane which goes through the points (2,-1) and…

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: Choose the parametric equations that represent the line segment that goes through the points (1,4,…

A: Given points x0,y0,z0=(1,4,-5) and x1y1,z1=(2,2,-1)

Q: I am working with cal 3. How do I find the parametric equations of the line for the intersection of…

A: The parametric equations of a line through the point (x0, y0, z0) and parallel to the direction…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: Given that z=x2+y2 and 3x−5y+7z=24 and point is 3,4,5. Let fx,y,z=x2+y2−z and gx,y,z=3x−5y+7z−24 We…

Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² = 4…

A: SOLUTION:

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

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

Q: A particle moves in space along a path whose parametric equations are given by bsin(wt), x2 =…

A: Image is attached with detailed solution.

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

A: The objective is to find the parametric equations of the line through the point.

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: 2: (a) Find parametric equations for the line through the point (-6, 1,2) and the point of…

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Q: 5. Find the distance from the point (3, 0, 10) to the plane 2x+3y+ z = 2. 6. Write the parametric…

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Q: Eliminate the parameter of the pair of parametric equations. x = 3t, y = t + 7 O y = 3x + 7 O y = 3x…

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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: Find parametric equations of the line containing the .point (2, 3,-1) and normal to the plane x+…

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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: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: Find the parametric equations for the line through the point P=(-5,4,-1) that is perpendicular to…

A: The equation of the plane is given by 2x-y-5z=0. The directional cosine of the normal to this plane…

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Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…

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: Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1)…

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Q: I need to get the parametric equation for a line between the points (0,1,2) to (3,0,-1). I have the…

A: Line passing though the points 0, 1, 2 & 3, 0, -1. Now let, x0, y0, z0=0, 1, 2 & x1, y1,…

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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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: Find set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular…

A: Normal vector perpendicular to the plane 2x−4y−2z=1 is: (2, -4, -2) The line passes through P = (-1,…

Q: 6. Find the distance between the point (- 3, 2, 1) and the line with parametric equations x = 3 –…

A: Consider a point on the line (3-2t, 1-t, -3t) which is the foot of the perpendicular to the point…

Q: Find the parametric equation for line l that is parallel to line m with equation: x = 1 + 4t; y = -…

A: Two lines are said to be parallel if their direction ratios are proportional. We will use this fact…

Q: y+3x-6z=8

A: answer is in next step

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

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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: Find parametric equations of the line through the point (8,3, 4) that is parallel to the plane -2x +…

A: The parallel line through the point has the vector equation L = < 8,3,4 > + t < a, b, c…

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

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Q: 5. Find parametric equations for the line of intersection of the planes x + y = 1 and y +z = 1.

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Q: Find a set of parametric equations for the line passing through the point       (1, 0, 2) that is…

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Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

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Q: Derive the parametric equations of the line of intersection of the two planes: II : x – 2y + z =1…

A: Given: P1:   x−2y+z=1P2:   2x−2y−4z=4

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.