Consider the plane P, that contains the points A = (1,2, –1), B = (3, 1, 2) and C = (2, – 1, 4). %3D (i) Find the Cartesian equation of the plane P. (ii) Find the distance from the point D = (3, –4, 1) to the plane P.

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

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: Write the equation for the plane. The plane through the point P(-2,-5,3) and normal to n = (2,7,8 O…

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Q: A. Find the angle between the planes x+y+z 1 and x-2y+3z 1, and Find symmetric equations for the…

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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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Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

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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,…

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Q: Find equations for the planes The plane through P0(0, 2, -1) normal to n = 3i - 2j - k

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Q: draw the plane given by the equation  x + y + z = 0

A: x+y+z=0 It is a plane passing through origin.

Q: Find an equation for the line that is orthogonal to the plane 3x- y+ 2z =10 and goec through the…

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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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Q: O Find an equation for the plane throught (l,-l,3) parallel to the plane 3x+y+Z=7

A: 1) To find the equation of the plane passing from (1,-1,3) and parallel to the plane  3x+y+z=7

Q: Find the intersection of the following geometric objects: the plane 3x + 2y - z = -9 and the line…

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Q: Consider the plane P with equation 2x+y-2z = 4 and line L with equations x =-5+2t Ly =-5+6t z = 4-4t…

A: Given equation of plane P is 2x+y−2z=4 and equations of line are x=−5+2t, y=−5+6t, z=4−4t. And given…

Q: Find the Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

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Q: Find the distance from the point (-2,0,3) to the plane given by the equation 3x+4y 5.

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Q: Find the distance between the points A(-5, -6, 2) and the plane that includes the y-axis and the…

A: As per Bartleby guidelines rule I am answering only first question as both question is not a…

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: Given the planes π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Find the equation of the…

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Q: Find an equation for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.

A: given that the plane passes through (-3,0,7) perpendicular to n=5i+2j-k. we need to find the…

Q: Q3: Find the distance between the origin and the plane containing the points A(1,1,0), B(-1,0,1) and…

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Q: Consider the plane P with equation -2x-2y+z=-3 and line L with equations x= 7-4t y = 7-6t z =-2-2t…

A: Use distance formula to find Q1,Q2

Q: Find an equation for the plane parallel to the liner =1- 21, y = 2 + 3t %3D 2 = 1+ 2t and that…

A: Given: Plane is parallel to the line x=1-2ty=2+3tz=1+2t Also, the plane contains the line of…

Q: Determine the general equation of the plane 2 passing through the point P (1, -4, -5) and parallel…

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Q: Find the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

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Q: Draw the plane given by the equation. x + y + z = 4

A: x+ y+ z= 4

Q: Find the x-, Y-, and z-intercepts of the plane. (If an answer does not exist, enter DNE.) 2x + 3y +…

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Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

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Q: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

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Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: Find an equation of the plane A through the point P(0,1,−1) and parallel to the plane B −x+ 2y+z=−3…

A: We will find the equation of plane a and the distance between two planes as following

Q: Consider the line L1 : ¤ = 3t, y =1+t, z=4+ 5t, and the plane II1 : -3x + y – 2z= 9. a) Find the…

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Q: Consider the plane P :r+y-z=0 in R that contains both the points P:(1,0,1) and P:(0, 1, 1). Answer…

A: The equation of the straight line passing through 2 points is , , .  Here, the points are .

Q: Write the equation for the plane. The plane through the point P(2, - 2, - 3) and parallel to the…

A: By the using properties we find the required equation of plane.

Q: Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = =…

A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: Consider the given diagram, find: (a) The coordinates of point R. (b) The exact distance from S to…

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Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

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Q: For the plane, 6x + 10y + 15z = 30, the values of the x-, y-, and z-intercepts are %3D 5, 3 and 2 3,…

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Q: Find the equation of the plane Π that contains the lines L1: x=−1−2s, y=1−t, z=−1+4s, s∈R…

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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 angle between the plane -2x +y-2z 0 and the plane generated by the points P1(0, 0, 0),…

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Q: Find the cosine of the angle, 0 Ses x/2, between the plane x +2y-2z= 2 and the plane 4y-5x + 3z =…

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Q: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

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Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: Find the intersection of the following geometric objects: the plane 3x - y + z = 3 and the plane 2x…

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Q: Consider the plane P with equation x+2y+2z=-7 and line L with equations x=-4-2t y=4+7t z=-1+3t…

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Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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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.