6) Consider the plane P : x+y – z = 0 in K³ that contains both the points P1(1,0, 1) and P2(-1,1,0). Answer the following questions: 6.1) Write down the parametric equations of the straight line L that contains both P and P2. 6.2) Use an appropriate system of linear equations to find the equation of the plane that contains the points P and P2, and is perpendicular to P.

Q: a) Find the best straight line fit to the given data points (-3,7), (1,–1),and (3,–7). b) Find the…

A:

Q: Find an equation of the plane with the given characteristics. The plane contains the lines given by…

A:

Q: Consider three points in three-dimensional space: А %3 (15, 2, —3), В %3 (2, —3, 15), С %3 (-3, 15,…

A: we know plane equation is <x-a, y-b, z-c>.n=0

Q: 3. Find the equation of the plane that includes the point (-1,0,7) and is parallel to the plane…

A:

Q: A)Find the equation of the XZ plane. B)Finde the equation of the plane ,each of whose points is…

A:

Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by the…

A:

Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PÓ and b= PR. Find (d) The…

A: Given three points are: P:-2,0,5, Q:3,1,1, R:0,0,4 The position vectors for the given points are:…

Q: B 10. Write a vector equation and parametric equations for a plane that satisfies each set of…

A: Due to Bartleby answering guidelines I have solved only first three Subparts of the given question…

Q: Find the equation of the plane that contains both of the lines given below. Line 1: x = 1+t, y = 2+…

A: Line 1 : x=1+t, y=2+2t, z=3-t        ⇒a⇀=1, 2, 3, l⇀=1, 2, -1 Line 2 : x=1-s, y=2+4s, z=3+2s…

Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

A:

Q: 2. Write the plane equation when it passes through a point Mo(11,2) and is: a) perpendicular to the…

A: We have to find the equation of the plane.

Q: Find an equation of the plane that passes through the point (1,2,3) and which is orthogonal to the…

A:

Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

A:

Q: 2. Give the parametric system of equations of the line given by the equations: 2x = 4 – 3y = ±1 Give…

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.