Given two planes: -3x + 2y – 4z – 3 = 0; x + 4y + 5z + 20 0. Find the symmetric equations of the line passing through the point (0, -3, -1) and is parallel to the line of intersection formed by these two planes.

Q: Find a line equation through the point P(3,-1,4) and parallel to the line of intersection of the…

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Q: А. Find the real number ( B ) such that the line of symmetric equations у-2 x- 3 = =3 is parallel to…

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Q: Find the equation of the plane through (1,-4,2) and per pendicular to each of the planes 2x t 5y -2…

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Q: Find the x-, y-, and z-intercepts of the plane. (If an answer does not exist, enter Di 4x - 5y + 2z…

A: for x intercept, y=z=0 for y intercept, x=z=0 for z intercept, x=y=0

Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line x-1=2, z=-63,…

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

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Q: x - 4y 10. dA, where R is the parallelogram enclosed by the lines x – 4y = 0, x - 3x - y

A: Given, the integral                   ∫∫R10x-4y3x-ydA Where R is a parallelogram enclosed by the…

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest…

A: Given planes, y+2z=12andx+y=6 Consider the point of intersection be x,y,z.

Q: 10) Find the equation of the line of the intersection of the planes 2x+3y+ 7z+23D0, x+2y-3z+ 5-0.

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Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = <1 , 3 , -1 >2x-y+2z=5vector b = <2 , -1 , 2 >

Q: The line (x-22-3, y = 2z) intersects the plane (x+3y-2+4= 0) at the point P, Find: a) the…

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Q: Q4. Find an equation of the plane that passes through the origin and the point (1,1,1) and is…

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Q: draw the plane given by the equation  12x − 6y + 4z = 6

A: To plot the graph of 12x-6y+4z=6, write the equation in terms of x and y for z and obtain…

Q: Solve the following and show the complete solution 1. Find the equation of the plane through (-3, 8,…

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Q: Find the point (if it exists) at which the following plane and line intersect. -2x-10y-10z = -19 and…

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Q: Find the point of intersection for the following three planes: x - 2y + z + 6 =0 2х + у — z + 2 %3D0…

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Q: ) Find the equation of line of intersection of the following planes 3x – 4y + 4z – 29 = 0 , 6x – 8y…

A: Explanation of the solution is given below...

Q: The quadrilateral ABCD on a coordinate plane has the following characteristics. AD can be…

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Q: Given the following equations: -3x + 6y + 2z = 1 6x - 12y - 4z = 17 Determine if the planes are…

A: -3x + 6y + 2z = 1..................(i)6x - 12y - 4z = 17 2(-3x+6y+2z)=-17…

Q: draw the plane given by the equation  x + 2y = 6

A: To draw the plane given by the equation  x + 2y = 6

Q: Given the point P (2, 4, -1) and the line L: x 1+ 2t; y =2-5t; z 2 +3t Find the equation of the…

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Q: Determine whether or not the planes f1:   3x  –  y  + z – 2 =  0 f2:     x + 2y –  z + 1 =  0 f3:…

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Q: a) Find the equation of line of intersection of the following planes 3x – 4y + 4z - 29 = 0 , 6x – 8y…

A: As per guidelines we are allowed to solve one question at a time. Kindly repost the rest question…

Q: Determine if the three planes -x-5y-5z= 2, 4x -5y +4z = 19 and x +5y - z = - 20 have an intersection…

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Q: Find the real number ( B) such that the line of symmetric equations ( x – 3 == ) is parallel to the…

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Q: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

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Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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Q: Find the equation of a) the line passing through the point (2, 1, 0) and parallel to the line X =…

A: Find the equation of (a) the line passing through the point 2,1,0 and parallel to the line x=5+2t ,…

Q: Find the distance between the parallel planes P1: 2x – y + 2z +6=0 and P2:6x- 3y+6z- 18 = 0

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Q: Find the point at which the line (-4, 1,1) + t(2, -5, 4) intersects the plane -5x+ 3y – 3z = -54.

A: the given line is  xyz=-411+t2-54 xyz=-411+2t-5t4t xyz=-4+2t1-5t1+4t

Q: (a) Find an equation for the line of intersection between the planes z+3y-z = 2 and 2x –y+2z = 5.…

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Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line X-1=と+2 3…

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Q: a). Determine a pair of planes whose intersection is the given line. = 2-3k, y = 3+e , Z- 2 -4€

A: Note: as per our guidelines we are supposed to answer only one question.* *Kindly repost other…

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

A: We have two equations in three variables. To find the line of intersection of these planes, we fix…

Q: Q/ Find the angle between the planes (x+y+2=1)and (x-24+32%-1).And find the Symmetric equations for…

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Q: Determine if the pair of planes are parallel: (a) 4x – y + 2z=5and 7x – 3y + 4z =8 (b) x – 4y – 3z –…

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Q: Find the intersection of the line and plane: x + 3y – 4z = 18, r(t) = (-3, 2, –2) + t(-3, 2, – 1)…

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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: 10 X- 3y dA, where R is the parallelogram enclosed by the lines x - 3y = 0, x - 3y = 5, 8x - y = 5,…

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Q: Find the equation of the line where planes Q and R intersect. Q: x-3y+2z=1 R: x+y+z=-1

A: To calculate the equation of line from the point of intersection of the planes Q and R. Where, the…

Q: Find the equation of the plane that passes through (3,4,-1) and contains the line of intersection of…

A: To work out the equation of the required plane satisfying the given geometric conditions

Q: Find the symmetric equation of the line that is an intersection of the planes a: x-4y + 2z-2 = 0 and…

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Q: 2. Find the equation of the line that is parallel to the intersection of planes 12, 2x-8y + z = 0…

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Q: Find the equation of the line of intersection of the planes 2x+y-2z = 1 and x+2y-z = 4.

A: Planes are 3-dimensional spaces, that contains infinite lines. When two non-parallel planes…

Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: Find the equation of the line of intersection of the planes: x+y+z=1, 2x+y-z=2

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

Q: Find the angle, in degrees, between the 2 planes with equations X-y+3z=1 and 3x+ y-z=D2

A: Take the normal vectors of the planes x-y+3z-1=0 and 3x+y-z-2=0 as N1⇀ and N2⇀ respectively.…

Q: Which of the following are symmetric equations for the line of intersection of the planes 2x+y+−6z=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.