(a) Find a vector parallel to the line of intersection of the planes 4x + 3y – 2z = -5 and -5x + y – 3z = 7. = (b) Show that the point (–1, -1, –1) lies on both planes. Then find a vector parametric equation for the line of intersection. 7(t) =

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

A: Given that a line . Find the parametric equation of the given line through point 1,0 and parallel to…

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

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Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

A:

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

A:

Q: If a line is parallel to the vector 2i + 9j + 8k and passes through the point P = (6, 8, 8), then…

A:

Q: Find the scalar equation for the plane passing through the point P=(-5, -2, –4) and containing the…

A:

Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A:

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: Find a scalar equation of the plane x + 2y + 3z = 0 -x+ 3y - 2z = 0 c. 13x + y - 5z = 9 d. 13x+y- 5z…

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Q: If a line is parallel to the vector 2i + 7j + 10k and passes through the point P = (6, 10, 5), then…

A:

Q: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

A:

Q: a line is parallel to the vector 2i + 7j+ 8k and passes through the point P = (3,6, 6), then the…

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

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 the scalar equation for the plane passing through the point P=(4, -5, 3) and containing the…

A:

Q: Find a parametric equation for the line that passes through points A (3,-2,4) and B (5,6,-2). x = 3+…

A:

Q: Find a vector parametric equation for the ellipse that lies on the plane 5y−3x+z=9 and is inside the…

A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

Q: (a) Find a vector parallel to the line of intersection of the planes -x + 3y + 4z : 0 and -x - 3y –…

A:

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

A:

Q: If a line is parallel to the vector 4i + 10j + 7k and passes through the point P = (7,7,4), then the…

A: Solution

Q: Find the scalar equation for the plane passing through the point P=(−4, 2, 10) and containing the…

A: Explained below

Q: Find a vector equation and parametric equations in t for the line through the point and…

A: Given that the point that posses through the line and the line perpendicular to the plane is, P 0 =…

Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

A:

Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: a) Find the scalar parametric equation and vector equation (r = c + ta) of the straight line z+5 x –…

A: We have to find

Q: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

A:

Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: SOLUTION-

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

A:

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

A:

Q: Find the angle between the two planes x- 2y + z = 29, 2x + 3y – 2z = 6. And also find the parametric…

A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: If a line is parallel to the vector 6i + 7j+ 2k and passes through the point P= (5, 1,7), then the…

A: Given that a line is parallel to the vector 6i+7j+2k and passes through the point P=5, 1, 7. We know…

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:   a) the parametric equation of the line determined by points A(1,0,2) and B(2.2.1). b) the…

A:

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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Q: Consider the line l in R³ given by the parametric vector equation 3 1 -2 -1 and the plane described…

A: Given that the line l in R3 given by the parametric vector equation and the plane described by the…

Q: Find the scalar equation for the plane passing through the point P-(0,-3, 2) and containing the line…

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: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: According to question given thatplanes equation 4x-y-3z=6-5x+4y-4z=3

Q: 9. (A) Find the parametric equations for the line through the point P = (-5, -1, -3) that is…

A:

Q: If a line is parallel to the vector 7i +9j + 9k and passes through the point P = (10,4, 1), then the…

A:

Q: If a line is parallel to the vector li + lj+ 4k and passes through the point P = (8, 4, 8), then the…

A:

Q: Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector…

A:

Q: 47. Determine the vector and parametric equations for the line passing through the points P(-1,-3)…

A: We’ll answer the 47th question since we answer only one question at a time. Please submit a new…

Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

A:

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² − 2x + 2y…

A:

Q: Q2 What are the parametric equations for the line through the point (6,-3,1) that is orthogonal to…

A: We have to find the equation of parametric line

Q: Find the parametric equations for the line of the intersection L of the two planes. 6x – 3y+ z = 5…

A: Parametric equations of the line is :  x(t) = x0 + a t  y(t) = y0 + b t  z(t) = z0 + c t  Here ( x0…

Q: (a) Find a vector parametric equation for the ellipse that lies on the plane 3x + 2y + z = -4 and…

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.