Consider the points P, Q and R with position vector (with respect to the origin O = (0,0,0)) d = (4, 1, –1), 6 = (2,5, 0) and d=(-1,6,4). (a) Compute the parametric and general (Cartesian) equation(s) of the line lị that passes through P and Q. (b) Give an equation for the plane B determined by P, Q and R. (c) Compute the distance of the origin O to the plane B obtained in part (b).

Q: 8. Find the parametric equations for the plane that passes through the points: P (2, -2, 3), Q (0,…

A:

Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: Find the equation of the plane passing through the point P(2, -1, 3) and perpendicular to the line…

A: We have to find the equation of the plane passing through the point  and perpendicular to the line…

Q: Determine parametric equations of the line of intersection of the planes x+2y+3z=4 and -2x+z=0. Then…

A: Let us consider two planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0  Intersection of two planes is line…

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: Let ū = (-2, –3) and d= (1,4). (a) What is the parametric equation of the line through i with…

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.