HW Problem 1: Find the standard equation of a plane that contains the point (1,2,3) and that is perpendicular to the line through (0,1,2) and (3,3,3).

Q: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: (a) Find the point at which the given lines intersect. (2, 2, 0) + t(2, –2, 2) (4, 0, 2) + s(-2, 2,…

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Q: b). Find the equation of the plane that passes by P(1, -2,3), Q(1,0,1), and the Origin O(0, 0, 0)

A: We have to find the equation of plane.

Q: Question 3. Find the point of intersection of the lines ix=--1-t, and then find the plane determined…

A: We have to find the intersection point of the lines and equation of plane passing through these…

Q: The Cartesian equations of the line perpendicular to the plane 2x -3y + 4z + 8=0 and passing:…

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Q: Find the general equation of the plane π  that passes through the origin and is perpendicular to the…

A: Suppose a plane passing through the points x1,y1,z1 and a vector perpendicular to the plane is…

Q: Find the general equation of the plane that contains the point (2,0,3) and the line r = -1+t, y =t,…

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Q: Find the equation for the plane through Po(4,9,8) perpendicular to the following li x= 4+t, y = 9+…

A: Given x=4+t  , -∞<t<∞y=9+2tz=-5tx=t=x-41 , y=t=y-a2  , z=t=-z5

Q: 29. In each case, determine whether or not the point lies on the line. If it does not, give an…

A: The line passes through the point B=3,-3,1 and has direction vector v→=4,4,1. Another vector in the…

Q: 4. Consider the lines 4: x=1+3ty=2+3t,z=3-10 and 1₂: a) Find the point of intersection of 1 and 2₂.…

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Q: Find the distance from the point (-1, -1, -2) to the plane - 3x – 2y + 1z = -4. Hint: See "Planes"…

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Q: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

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Q: find the equation of the plane through P(1, 3, 2) that is parallel to the plane 5x - 4y + 3z = 7

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Q: 4. Consider the points A(1, 0, 3), B(-1, 5, 2) and C(3, -1, 1). Find the equation of the plane…

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Q: Question 4 2 pts Find the point of the intersection of the plane P: 2х — Зу + 42+14- 0 and the line…

A: Given that  The plane and the line  To find the point of intersection of the plane and the line

Q: 1. Find the equation of the plane that contains the following points. (2, –1, 4), (3, 2,0), and…

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Q: 9. Write an equation of the plane that passes through (2,0, –3) and (a) is perpendicular to the line…

A: Given: The vectors are: a=-1, -2, 3b=3, 0, -2v=2, -5, -4 The equation of plane is, P=2x+y=z+13

Q: 15. Find an equation of the plane through the point (-2, 4, 6) and perpendicular to the line r = t,…

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Q: Find the general equation of the plane that contains the point (2,0, 3) and the line r -1+t, y =t, z…

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Q: Find an equation for the plane that contains the line x = − 1 + 3t, y = 5 + 3t, z = 2 + t and is…

A: We need to determine the equation of the plane that contains the line: x=-1+3t, y=5+3t, z=2+t and is…

Q: 1. Find the equation of the plane that contains the line point (1,3, 2). 무 =D북3부 md the

A: Let's find.

Q: Find the Cartesian equation of the plane containing the points A(- 1,0, 1), B(2, 1, 3), C(4, – 2,…

A: topic - equation of plane through three points

Q: Question 4 2 Let L be the line with the equation -3 +t 2 and let II 4 3 be the plane with equation…

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Q: Determine the equation of the plane that contains the points P_0 = (1, 0, 0), P_1 = (0, 1, 0) and…

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Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

Q: Find the standard equation of the plane that contains three points A(1,0,-1) B(2,1,1) and C(1,2,-3).

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Q: Problem 1: Let P, be the plane defined by the equation 2x – 8y + 5z = 2 and let P2 be the plane…

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Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line X-1=と+2 3…

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Q: Find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R = (2,…

A: To find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R =…

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

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Q: (1) Find an equation of a plane that goes through (-1,2,6) and is perpendicular to (2, 1, –3).

A: It is given that the perpendicular vector to the plane is given as,  and plane passing through,…

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

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Q: An equation of a plane P passes through the point (0,0,3) and perpendicular to the line L:x =1– 2t,…

A: Given,          An equation of a plane P passes through the point 0,0,3 and perpendicular…

Q: Problem 2. Find an equation for the plane that passes through points (1,4, 1), (1, 7,3), (3, 9, 1)

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Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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Q: -1. Through (1,5, 2) perpendicular to 37 – J + 4k .

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Q: Find the equation of the plane passing through the points A(2,2,1), B(9,3,6) and perpendicular to…

A: Here we have to find the equation of the plane passing through the points A(2,2,1) ,B(9,3,6) and…

Q: The general equation of the plane that containsteh points (1,0,3),(-1,1,-3)and the origin is of the…

A: Given general equation of plane is

Q: Find the equation of the plane that contains the point A(1, 2,-4) and is perpendicular to the…

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Q: - Find the equation of the plane that passes through the three points A(1,0,0), B(0,2,0), and C(0,0,…

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Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).

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Q: Find the equation of the plane that contains the points P(-1,2, 1), Q(0, -3, 2), and R(0, 1,-4)

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Q: Question 1 Find the equation of the plane through points P1(-2,1,4), P2(1,0,3) that is perpendicular…

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Q: The general equation of the plane that contains the points (1, 0, 3), (-1,1,-3), and the origin is…

A: Explanation: Given that,  equation of plane ax+by+cz=0and (1,0,3), (-1,1,-3) and (0,0,0) on the…

Q: Question 4. Find an equation of the line of intersection of the planes -x+2y+z= 1 and x+y+z=0.

A: This is a problem related to geometry. Based on the general formula and concept we will answer the…

Q: 29. In each case, determine whether or not the point lies on the line. If it does not, give an…

A: Since we have given a point and a line -

Q: The equation of the plane passing through the point A(4, 9, 4) and orthogonal to the line a = 9 +…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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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.