(a) Obtain parametric equations for the line passing through the points A(9, 2,8) and B(-21, 7, –2). (b) Find the Cartesian equation of the plane 1 that contains the points P(1,9,2), Q(2,7,1) and R(7,1, -3). (c) Find the angle between plane 1 and plane 2: –3x + 2y + 4z = 5. (d) Find the point of intersection between the line in (a) and plane 1.

Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

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Q: Find a set of parametric equations for the line passing through the point (2, 0, 9) that is…

A: a set of parametric equations for the line passing through the point (2, 0, 9)  that is parallel to…

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

A:

Q: 12. Find the parametric equations of the line that contains the point P and intersects the line L at…

A: Given equation of the line is  L:x=-2+2t , y=4+2t , z=2+t          Then, the co-ordinate of any…

Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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

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

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: a +…

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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: Q1) (a) Find the parametric equations of the line L that passes through (3, −2, 1) and is…

A: we need to find  the parametric equations of the line L that passes through (3,-2,1) and is…

Q: (a) Show that the parametric equations x = X1 + (X2 - X1)t, y = y1 + (y2 – Y1)t where 0 sts1,…

A: Given Points are P1(x1,y1) and P2(x2,y2)

Q: Find the parametric equations of the line of intersection of the planes, and find the angle between…

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Q: Find the point P of intersection between the line x(t) = (-3,-2, 1) + t (1, 1, -3) and the plane 4z…

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Q: Find the parametric equations for the line in which the planes x-2y+4z=2 and x+2y-2z=6 intersects

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Q: Find parametric equations for the line through P0 = (3, −1, 1) perpendicular to the plane 3x + 5y −…

A: A line L in sace with direction vector d=d1,d2,d3 that asses throughthe point P=(x0,y0,z0) can be…

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: 4. (a) Find a parametric equation and symmetric equation of the line that pases through the point…

A: We have a point P(2,-1,3) and a vector  i^+2j^-3k^ We have to find a parametric equation and…

Q: Find the point at which the line given by the parametric equations below intersects the plane.…

A: Given a system of linear equations are, 2X + 4Y -3Z =-48.................(1) X = 10 +…

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

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

A: The parametric equation of a line passing through the point and has a direction cosines <a , b…

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

A: we know that equation of line in parametric form which passes through pointx1,y1,z1 and…

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: 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: Complete the parametric equations of the line through the point (4,-8,3) and perpendicular to the…

A: See this solution in below

Q: 30. Determine two sets of parametric equations for the line passing through the points P( 1,7, 1)…

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Q: a) Find the parametric equations for the line in which the planes x-2y+4z=2  and x + 2y - 2z = 6…

A: Consider the provided question, (a)

Q: Find parametric equations for the line segment joining the points (-6, 4) and (2, 3). x=-6 + 8t, y =…

A: Parametric equation of line segment.

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

A:

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

A:

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: Find the parametric equations for the line of intersection of the planes x+y-z = -20 and 9.x + 3y +…

A: Given planes, x+y-z=-20 and 9x+3y+z=16. The objective is to find the parametric equations for the…

Q: 4 /5 . 135% + - (a) Find parametric equations for the line of intersection of the planes x+2y- = 3…

A: In X plane, put y=z=0 & in Y plane put x=z=0 &in Z plane put x=y=0

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

A:

Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

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 a parametric equation for the line through the point (- 1, - 5, - 2) and perpendicular to the…

A: The parametric equation of the  line through the  points P0x0,y0,z0 and Plane a, b, c is x=x0+at…

Q: Find the parametric equations of the line L2 that passes through the point P(-9, 1, -6) and is…

A: Given that the line L2 passes through the point -9,1,-6 and is parallel to the line given parametric…

Q: It can be shown that the parametric equations I = x1 + (x2 – r1)t, y = Y1 + (y2 – Y1)t, where 0 < t…

A:

Q: 2. Find the parametric equations for the line through (3, –2,5) and (2,3,0). 3 Find the equation of…

A: To find the parametric equation for the line through 3, -2, 5 and 2, 3, 0

Q: 6) Find the following: a) An equation of the plane passing through the points P(2,1, 10, Q(-1, -1,…

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Q: Provide parametric equations for the line passing through the coordinates (1, −3, 2) and…

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Q: 277. Find parametric equations of the line passing through point P(-2, 1, 3) that is perpendicular…

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

A:

Q: Find the requested equations below Parametric equations of the line that contains the point P(3, 4,…

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Q: Find the equation for the plane that passes through (2,4,-1) and contains the intersection of the…

A: The plane equation Ax+By+Cz+D=0 passing through three points x1,y1,z1, x2,y2,z2 and x3,y3,z3 is…

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: Find parametric equations for the line described below. The line through the points P(- 1, - 1,4)…

A:

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.