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

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Q: Given the points A(7, -2, -9 ) and B( 7, −2, 2 ). Question 3 a) [:] Write parametric and symmetric…

A: We have to find the equation of line and intersection of line and plane.

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

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

A: Direction angle

Q: 3+z Given the points R (1, -1, -3), the vector v = and the line d: ¯x+¹=1+y= 3 2 3. Calculate the…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Question 1 ( Consider the points A(2,-1,0), B(-3, 0, -2), and C(0, 3,-1). (b) Find the parametric…

A: Since A≡(2,-1,0), B≡(-3,0,-2) and C≡(0,3,-1). So AB→=-5i+j-2k, AC→=3i+4j-k and BA→=5i-j+2k. Thus…

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: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

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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: 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: 9. (a) What are the two properties that determine a line in space? Give parametric equations for a…

A: To find the parametric equations for the line through the given points and to mention the properties…

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…

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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.