Find the equation of plane through (5, 4, -1) and perpendicular to each of the planes            x-y+2z-3=0      and  2x-3y+z=0

Q: 1. Find the equation of the plane that contains the point (-1, 1, 2) and the line given by x=1-t,…

A: This question is based on 3d geometry.

Q: find the plane containing the intersecting lines.  L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

Q: Consider the two lines Lı : x = 2- 3t, y = -1+ 2t, z = and L2: r = 2+ s, y = -1- 3s, z = that…

A: We will find out the required equation of plane

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

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

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 plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞<t<∞L2: x=1-4s,y=1+2s,z=2-2s;…

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 point P where the line x = 1+t, y= 2t, z= -3t intersects the plane x+ y -z = -3

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Q: Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets…

A: Given that the line is passing through origin so ro = (0,0,0) and perpendicular to the plane 2x – y…

Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2)…

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Q: which of the following is the equation of the plane that is passing through the point P(2,2,-2) and…

A: Given P( 2, 2, -2) and planes  x+2y-3z=3 and x+y+z=2

Q: Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the…

A: Topic = Vector correct answer e

Q: Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y…

A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: Find an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t D)= O…

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Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: 1. Find the equation of the plane containing the lines L1 and L2 given below: z = 4t + 3 z = -4s – 1…

A: Given :L1:  x=2t+1, y=3t+2, z=4t+3L2 : x=s+2, y=2s+4, z=-4s-1

Q: Find the plane containing the intersecting lines x = -1+t, y = 2+ t, z =1–t; -0 <t < o∞ | L2: x = 1…

A: Find the planes containing the intersecting lines: L1:x=-1+t,y=2+t,z=1-t for all…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2, –2)…

A: The equation of the plane passing through the points (x0 , y0 , z0) and perpendicular to a vector…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: The equation of the plane through P.(2, 4, :5) perpendicular to the line :X = 5 +t ,Y= 1+ 3t , Z= 4t…

A: (.)  Let the point Px1,y1,z1 and perpendicular line  x-x0a=y-y0b=z-z0c Then the equation of the…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: Find the point of intersection of the line x = 2 − 3t y = 4 + 2t −∞ &lt; t &lt; ∞, z = 3 − 5t, and…

A: x=2-3ty=4+2tz=3-5tand the plane 2x+3y+4z+8=0

Q: Find the point in which the line through the (3,-1,2) perpendicular to the plane x +2y -5 z = 4…

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Q: Let L be the line whose symmetric equations are x-1=1=z+1. The equation of the plane through the…

A: Given: Symmetric equation of line L: (x-1) = (y-1)/9 = (z+1) Point P(2,3,-1)    To find: Equation of…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Show that the line through two distinct points (x1, y1) and (x2, y2) in the plane has equation: | x…

A: Solution..

Q: Find the symmetric equations of the L that is parallel to the two planes x + 2y - z= 2 and x + 6y+ z…

A: Given: Two planes, P1: x+2y-z=2, P2: x+6y+z=-3, Point P1, 2, 3

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are &lt;2,-1,2&gt;, since line is normal to…

Q: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: 2) Find the equation of the plane that is orthogonal to the planes 3x-2y-2z=1 and x-3y-10z = 4 and…

A: Given: The equation of two planes 3x-2y-2z=1 and x-3y-10z=4 and the equation of one line…

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

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: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

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Q: 11. z = 1+ 2t 3x + 11y - Find an equation for the plane parallel to the line x = 1-2t, y = 2+3t and…

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: Find the plane determined by the intersecting lines. L1 x= - 1+ 3t y =2 +3t z =1- 4t L2 x= 1-4s y =…

A: Given :-  The plane determined by the intersecting lines. L1    :   x = -1 + 3t    ,    y = 2 + 3t…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A: The line L is perpendicular to the plane, x+2y+4z = 0 Hence the direction ratios of the line L is…

Q: Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 and…

A: Your line, perpendicular to the plane will have the slope of &lt;2, -1, -1&gt;, and passes through…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

A: To find the equation of the plane passing through the point P 2,2-2 and vertical to the line of…

Q: -1 Consider the lines lį : ,- 2 1- x z - 3 = 2– y = =+1 and lz :5- y - 2=. %3D 2 3 Find the equation…

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Q: Find an equation of the plane that contains the point (2,0,-8) and contains the line y- 2 z+1 x +4 =…

A: The plane passes through the point 2, 0, -8. Thus, the equation of the plane can be written as…

Q: Find an equation of a plane containing the line r=⟨0,−5,−1⟩+t⟨−2,4,−2⟩ which is parallel to the…

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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 an equation of the plane perpendicular to each of the planes z – y+z = 0 and 2r+y-4z–5 =0 and…

A: The given problem is to find the equation of plane perpendicular to each of the given planes and…

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 passing through the point P(1,-1,2) and parallel to the lines =Dz and…

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Q: Does the line r(t) = intersect the plane 5x - 2y - z = 21 and if so, where?

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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.