find the distance from the point to the plane. (0, -1, 0), 2x + y + 2z = 4

Q: Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r:…

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Q: Find an equation of the plane.  The plane through the point (2, 0, 5) and perpendicular to the line…

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Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

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Q: Find an equation of the plane through the point (2, 0, 1) and perpendicular to the line x = 3t, y =…

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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 equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t 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 an equation of the plane. The plane through the point  (6, 0, 1)  and perpendicular to the line…

A: Given, The plane through the point (6, 0, 1) and perpendicular to the line x = 7t, y = 8 − t, z = 5…

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: Find the equation of the plane through the point (2, 4, 3) that is perpendicular to the line r = (2i…

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Q: Find the point in the plane 2x − y + 4z = 16 that is closest to the origin.

A: Given:     Plane 2x-y+4z=16 Distance of point P(x1,y1,z1) from plane Ax+By+Cz=D is…

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 equation of the plane perpendicular to the x-axis and passing through the point (3,-3,2)…

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Q: Find the equation of the plane through the point (2, –1, –5) and containing the line | x = 3 – 2t, y…

A: We have to find the equation of the plane, passing through the point (2,-1,-5) and containing the…

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: Find the equation of the line that contains the point (1,–1, 2) and is perpendicular to the plane 2x…

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Q: Q1 What is the distance between the point (2,8, 5) and the plane r- 2y-2z = 1 ? a) 5 b) 25 c) 9 d) {…

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Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

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Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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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: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

Q: Find an equation of the plane through the point (2,0, 1) and perpendicular to the line x = 3t, y = 2…

A: To find the equation of a plane passing through (2,0,1) and perpendicular to the line x=3t , y=2-t ,…

Q: Find an equation of the plane that contains the point (2, 0, 3) and the line x =-1+t, y =t, z=-4+21…

A: It is given that the required plane contains the point 2,0,3 and the line x=-1+t,y=t,z=-4+2t. The…

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

A: given plane pass through the point(3,-1,4)

Q: Find an equation of the plane. The plane through the point (-3, 9, 10) and perpendicular to the line…

A: Find the equation of the plane

Q: Find an equation of the plane. The plane through the point (4, 0, 2) and perpendicular to the line x…

A: To find- Find an equation of the plane. The plane through the point 4, 0, 2 and perpendicular to the…

Q: Find the equation of the plane through the point (2, 4, 3) that is perpendicular to the line r = (2i…

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Q: Find an equation for the plane that passes through the point (1, 3, -5) and is perpendicular to the…

A: Given point is (1,3,-5). The scalar equation of a plane that passes through point (a, b, c) and has…

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: Find the equation of the plane through the point P = (3, 2, 5) and parallel to the plane a + 3y+ 3z…

A: Given: Line is parallel to x+3y+3z = 5 Equation of the plane parallel to the plane x+3y+3z = 5 is…

Q: Determine the x coordinate of the point on the plane Π:−3x−2y+2z=2 closest to the point (2,5,−5).

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Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

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Q: Find the equation of the plane for all points equidistant to (1, -1, 1) and (0, -5, -2).

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Q: Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x…

A: Direction ratios of line x =-1 + t, y = 6 - 2t, z = 3t are  <1,-2,3> .Sine line is…

Q: find the point in which the line meets the plane x = -1 + 3t, y = -2, z = 5t; 2x - 3z = 7

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Q: Find the equation of the plane contains the line x=3t,y=1+t, z=2t, and parallel to the line of…

A: Given, the plane contains the lines x = 3t, y = 1 + t, z = 2t and parallel to the line of…

Q: Write the equation for the plane. The plane through the point P(-4, -1, -6) and perpendicular to…

A: GIVEN: Point P (-4, -1, -6)  Line x = 10 + 4t, y = 7 + 3t, z = 1 + 5t

Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is  x+2y-10z+12=0 We need to find the equation of plane that is…

Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

Q: Find the equation of the plane through the point P = (5, 3, 3) and parallel to the plane 3y – 5x –…

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Q: Find the equation of the plane that contains the point P(-6, 5, 7) and is perpendicular to the line…

A: Use direction ratios of line to find direction ratios of plane. Then use the point to find equation.…

Q: Find an equation of the plane. The plane through the point (-3, 7, 10) and perpendicular to the line…

A: Given:- The plane through the point (-3, 7, 10) and perpendicular to the line x = 5 + t, y = 2t, z =…

Q: Find the intersection of the plane 3x – y + 2z – 3= 0 and the line

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Q: Find the distance between the parallel planes P and P P: 2z -y+ 3z -6 =0 P: 4z - 2y + 6z - 2 =0

A: Distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is…

Q: Determine the cartesian equation of the plane having x-intercept of 2, a y-intercept of 5 and a…

A: To find the cartesian equation of the plane

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.