Find the real number ( B ) such that the line of symmetric equations x - 3 = 2 у-2 = is parallel to the plane of equation (–2y + 4x = ßz + 10 ) -2

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

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Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y Z…

A: The plane passes by P2,0,-1 and that is perpendicular to the line x-5-2=2-y4=z-23

Q: Represent two planes that intersect at a line represented by 3. y- 7 = z+2 2.

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Q: Find a set of parametric equations of the line with the given characteristics.

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Q: 2. Find an equation of the plane parallel to the line

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Q: Find an equation of the line through (-2, 5, 3) that is perpendicular to both u = (1, 1, 2) and the…

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Q: What is the equation of the plane through (-1,-1,-1) parallel to the plane x+ 2y + 3z = 9?

A: The vector normal to the plane ax+by+cz=d is ai^+bj^+ck^ . The plane parallel to this plane has the…

Q: Find a set of symmetric equations for the line “A" perpendicular to the lines having direction…

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Q: 4) Find the equation of the line of the intersection of the planes -2x+3y+7z+2=0, x+2y-3z+5=0.

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Q: Find an equation of the plane containing (1, 5, -1) that is perpendicular to the line of…

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Q: find the equation of the plane passing through(1,0,-1)&(-1,2,1) and parallel to the line of…

A: To determine: The equation of the plane passing through the points (1, 0, -1) and (-1, 2, 1) and…

Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: 3- Find an equation of the Plane perpendicular to the line through (2,2,-9) and (7,-1,3) and…

A: To Find: Equation of plane perpendicular to the line through the points (2,2,-9) and (7,-1,3) and…

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

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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: Find the equation of the plane that contains the line x-y+z=2 , x+y+2z=D4 and the line 1= = 2-7

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Q: Find the equation of the plane through (-1,6,2) and perpendicular to the join of (1,2,3) and…

A: We have to Find the equation of the plane through (-1,6,2) and perpendicular to the joining of…

Q: Find the distance from point P(2, 7, -6) to the plane of equation 5x - y + 4z - 8 = 0

A: We have to find distance

Q: XIV. Give equation of straight line through point (1,3,-2) perpendicular to z = Зх-2y +4.

A: Given z=3x−2y+4 and point is x0,y0,z0=1,3,−2 We have to find the equation of straight line through…

Q: Find an equation of a plane through the point (1, -4, -3) which is orthogonal to the line x = -3 –…

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Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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Q: 3. What is the equation of the line that passes through point (-3,-1) and is perpendicular to the…

A: Given that: The given equation of the line is y=-13x+5 and the given point is -3, -1 So, we have to…

Q: The equation of plane through the origin and parallel to the plane 2x +5y-4z = 8 is 2x + 5y- 4z = 0.

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Q: Find an equation of the plane through (-8, –4, –5) that is 2 = t, y + 3 | perpendicular to the line…

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Q: The plane that passes through the point (5,2,2) and is perpendicular to both x-5z=-24x-5z=-24 and…

A: The direction ratio of the normal vector to the plane x-5z=-24 or x+0y-5z=-24 is (1,0,-5) The…

Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

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Q: Find the symmetric equations of the line that passes through the points (-2, 1, 0) and (1, 3, 5).

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Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

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Q: 3. Through the point (4, -5, 20) and perpendicular to the plane x + 3y – 6z - 8 = 0.

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Q: Find equation of the line passing through the point (4, 2, 6) and parallel to the line of the…

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

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Q: Find an equation of the plane through (1,3,–2) and the line of intersection of the two planes with…

A: Given that, Point A (1,3,-2) Two planes  P1: x-y+z-1=0P2: x+y-x-1=0   We have to find the equation…

Q: Find the equation of the plane that passes through the points A = (1, –4, –1), В - (-5, —3, —5), and…

A: Proceed as shown below

Q: . Find an equation of a plane passing through the point (3, 4. 0) and containing the line of…

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Q: (-2,4) parallel to y=-3/2x+3

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Q: 4 Determine whether the straight air routes with equations x-=-3 and x =-5 are 2 intersecting or…

A: Given,  The equation of the straight lines are x - y/2 = -3  and x = -5

Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

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Q: Find equation of the plane through (1,0,-1).(-1,2, 1) and parallel to the line of intersection of…

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Q: Find the equation of the plane through the points (1, -1, O), (1, 0, 1) and (2, 2, 1).

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Q: Find a plane containing the point (1,-8,-3) and the line of intersection of the planes - 3x – 8y +…

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Q: Find the equation for the plane through Po(-5, - 8,8) perpendicular to the following line. x= - 5-t,…

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Q: Find the equation of the Line passing through the point (2,-4,1) and parallel to the plane 3x+y-2z=5…

A: Given plane , 3x+y-2z=5 -i whose directionof the normal to the plane is3,1,-2and given equation of…

Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

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Q: find the equation of the plane passing through (1,0,-1)&(-1,2,1) and parallel to the line of…

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Q: Find the equation of the plane through (-6,5,-1) and is parallel to the xy plane

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Q: Write the equation of the plane passing through point (3, 8, 3)| that is parallel to the xz- plane..

A: Given: A plane passes through (3, 8, 3) and is parallel to the xz-plane. To Find: Equation of plane

Q: 4] Find the equation of the plane that contains the point (а, 0, 0), (0, b, 0) and (0, 0, c).

A: First find two vector and then take cross product which is normal vector  Now use equation of plane

Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

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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.