Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the plane of equation 2x + 3y – 5z = 0.

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

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 distance from the point to the given plane. (1, -4, 6), 3x + 2y + 6z = 5

A: Given:   3x + 2y + 6z = 5     Point: ( 1 , -4 , 6 )

Q: Q1// A :- Find an equation of the plane that passes through point (1,4,3) and contains the line…

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Q: Find the equation of the plane passing through the points (1,0, -1), (-1,2,1) and parallel to the…

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Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

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: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x= -6+t, y…

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Q: Find the equation of the straight line passing through (1, 2, 3) and perpendicular to the plane x +…

A: Given:       Equation of the straight line passing through  (1, 2, 3) and perpendicular to the…

Q: Find the equation of the plane passing through the point (-1, 4, 0) perpendicular to the line L₁: x=…

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Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: Find the distance from the point Q(1, 2, -4) to the plane 2x - 5z = 5.

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Q: 6. Find the equation of the plane that passes through (3,1,2) and (-1,2,–1) and is parallel to the…

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Q: Find the distance from the point (0, -1, -2) to the plane - 4y – 4z = 5.

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

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Q: Find the distance from the point (-1, 3, -1) to the plane -1x + 2y -5z=1.

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

Q: Find the equation of the plane through the point (1,2,-1) and parallel to the plane 2x- 3y+4z+6-D0.…

A: To find: The equation of plane passing through the point 1,2,-1 and parallel to plane 2x-3y+4z+6=0.…

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 for the plane parallel to – 2x + 9y – 2z 30 and containing the point (1, 4, 3)

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Q: find an equation of the plane passing through the three points given.  P = (2, 0, 0), Q = (0, 4, 0),…

A: Equation for plane P is written in vector form as: n.(x,y,z)=d In scalar form equation is written as…

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: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: The plane containing the point (0,7,-2) and parallel to the plane -x + 8y + 6z = Ax+By+Cz = D. 4 has…

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Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

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Q: Find the distance from the point to the given plane. (1, -2, 4), 3x + 2y+ 6z= 5

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

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: Find an equation of the plane containing the lines given by 1-x = y = z+ 1 2 and * = y – 1 = z - 2…

A: From the given problem:, the plane containing lines are: 1-x2=y=z+1andx+1-2=y-1=z-2 So we can simply…

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y+3…

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Q: Suppose we need to find an equation of the plane that passes through the line of intersection of the…

A: Since, we know that equation of a plane passing through the intersection of planes P and Q is given…

Q: Find the equation of the plane containing the point (4, -1, 3) that is parallel to the plane 2x - 3y…

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Q: Find the distance from the point to the given plane. (1, -3, 4), 3x+2y+ 6z = 5

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

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Q: Q1/ Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to…

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Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

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

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Q: Find parametric equations for the line in which the planes 3x - 6y -2z = 15 and 2x + y - 2z = 5…

A: Equation of plane - 1,3x-6y-2z = 15 Normal vector of plane 1 = n1 = 3,-6,-2…

Q: . Find symmetric equations of the line that is normal to the plane x-3y+2z =12 at the point where…

A: On the z-axis points are of the form (0,0,z)  We plug this in the given plane to find z So the line…

Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1…

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: The intersection point of the line whose equation is (x+2y+z=1),(x+y+2z=-1) with the xz plane is:

A: we have given x+2y+z=1  ...(i)x+y+2z=-1  ...(ii)solve it  2×(i)-(ii)x+3y=3   ...(a) this is equation…

Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the…

A: consider the direction ratio of line  contaning the point ( 1, 2 ,1 )  is  l , m, n

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 an equation of the plane through (4, 1, –4) that is perpendicular to the line x – 2 = 5t, y+3 =…

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Q: Find an equation of the plane through (-8, 4, –9) that is perpendicular to the planes 5x – y +z = 1…

A: Solution of question is written in below steps.

Q: Find the equation of the plane passing throught (0,0,-4) and perpendicular to the line joining the…

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Q: Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane…

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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: Find an equation of the line normal to the plane containing the line I-2 y+1 %3D and +1 - y+8 %3D 3…

A: The given problem is to find the equation of line normal to plane containing the lines at their…