(a) Find a parametric equation and symmetric equation of the line that pases through the point (2, -1,3) and is parallel to the vector 7+27-37. (b) At what points does this line intersect the yz-plane?

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

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Q: Find parametric equation for the lines .. The line through (0, -7, 0) perpendicular to the plane x +…

A: A parametric equation of a line can be written if a point on the line is given and a vector parallel…

Q: A) Find the parametric equations for the line through the point P = (3.-5, 1) that is perpendicular…

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Q: 1) Find parametric equations for the line which contains A(2,0, 1) and B(-1,1, –1).

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Q: Find parametric equations for the lines in The line through the point P(3, -4, -1) parallel to the…

A: Given P3,-4,-1r=ro+tvro=3,-4,-1,ro=3i∧-4j∧-k∧v=i∧+j∧+k∧

Q: Complete the parametric equations of the line through the point (-6,0,-8) and perpendicular to the…

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Q: Find the vector and parametric equations for the line through the point P(-5, -3, -4) and the point…

A: Given: P(-5,-3,-4) and Q(-2,2,-5) To find the vector r(t) and the parametric equations for x(t),…

Q: Write the equation of the line passing through P with direction vector d in vector form and…

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Q: Find parametric equations for the lines in The line through (2, 4, 5) perpendicular to the plane 3x…

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

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Q: Find parametric equations of the line that is perpendicular to both i = (1,0,0) and i = (1,1,1) that…

A: Given that: i=<1, 0, 0>v=<1, 1, 1>and P(1, -2, -1)

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

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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: Find the vector equation and parametric equations of the line passing through the point P(5, 6, 7)…

A: Given problem :

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

A: Line passing through the point 6, -6, 8 and perpendicular to the plane 7x+2y-3z=-8. Since the line…

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 parametric equations of the line perpendicular to l1 and l2 that contains the point (-1.…

A: We have to find equation of a line which is passes through the point (-1,-1,-1) and Perpendicular to…

Q: Find parametric equations for the line through (-2, 0, 4) parallel to v = 2i + 4j - 2k

A: we know that parametric equation of line which passes through point x0,y0,z0 and parallel to vector…

Q: How do you find the parametric and symmetric equation of the line passing through the point (3, 2,…

A: We have to find the parametric and symmetric form of the line perpendicular to the given plane at a…

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

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Q: d) Find the parametric equations for the line of intersection of the two planes.

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Q: The angle and the parametric equations for the intersect line between planes a + y = 1, and 2r+y-2z…

A: Given, x+y=1, 2x+y-2z=2 we know angle between two plane is…

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

A: We need to find the vector equation of the line of intersection. In order to get it, we’ll need to…

Q: 5. Find the parametric equations of a line through (1, 0, -1) and parallel to the line -(x-4) 1 y =…

A: Consider the given equation of the line. Converting it into the standard form and taking the…

Q: Determine the vector and parametric equations of the line through A(6,2,5) and B(9,2,8)

A: Given points , A(6,2,5) B(9,2,8) Therefore a=6i+2j+5k b=9i+2j+8k

Q: Find a parametric equation and symmetric equation of the line that pases through the point (2, -1,3)…

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Q: Find the parametric equations of the line segment through the origin and perpendicular to the plane…

A: Given: Given equation of the plane is x-2y+3z=5 We want to find the parametric equations of the line…

Q: Find the parametric equation of the line that passes through the point (4, -5, 0) and is…

A: We have to find the parametric  equation of the line.

Q: Consider the line which passes through (1,-2,-2) and (2,0,1) (a) Write a vector equation, a…

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Q: Find a set of parametric equations and symmetric equations of the line ` con- taining the point P(1,…

A: Given Point is (1,-2,3) And Plan is : 2x-y+3z=6

Q: Q.1 Find the parametric equation of the line that 2)Passes point (1,3,7) and orthogonal to xy-…

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Q: b) Find parametric equations of the plane (P) containing the point P(1,-2, 0) and the vectors û and…

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Q: Find parametric equations for the line in which the planes 3x - 6y -2z = 15 and 2x + y - 2z = 5…

A: Equation of plane - 1,3x-6y-2z = 15 Normal vector of plane 1 = n1 = 3,-6,-2…

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: Complete the parametric equations of the line through the point (3,-7,-2) and perpendicular to the…

A: Given that, the equation of the plane is     -3x-y+z=2  and the point (3,-7,-2) The direction vector…

Q: Find the parametric equations for the line through the point (5, 2,9) and perpendicular to the plan…

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Q: Find the symmetric and parametric equation of the line that is the intersection between the planes…

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Q: (a) Find a parametric equation and symmetric equation of the line that pases through the point (2,…

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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: B Find the parametric equation of the plane passes through the point (-3,0,7) and perpendicular to…

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Q: A) find a vector parallel to the line of intersection of the planes -3x - 2y - 2z = -1 and -4x - 2y…

A: Equation of line of intersection

Q: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

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Q: 1. a. Show that two lines with direction vectors d (2,3) and d, (6,-4) are perpendicular %3D b. Give…

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

A: Note:- As per our guidelines, we can answer the first of this problem as exactly one is not…

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

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Q: omplete the parametric equations of the line through the point (-3,2,4) and parallel to the vector -…

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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.