Find a line equation through the point P(3,-1,4) and parallel to the line of intersection of the planes 3x-5y+2z%3D1, 2x+y-z=-2. 3+3t A y= -1+7t , - 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: Find the equation of the plane through (-1,4,2) and containing the line of intersection of the…

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Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

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Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

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Q: The plane equation that has 3.9 units distance to the plane 5x -2y + 3z= 4 is O a. 5.0x-4y+3z=56.1 O…

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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: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

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

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

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: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: The Cartesian equations of the line perpendicular to the plane 2x -3y + 4z + 8=0 and passing:…

A:

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

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Q: Find the line of intersection of the given planes. 4x + y-z = 0 and 2x - y + 3z 4 %3D

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

A: The parametric equations of the line x=3y=4z may be re-written as  so that its vector equation is…

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 that passes through the point (-1, 4, 2) and contains the line of the…

A:

Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

A:

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

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Q: The plane through the points (2, 1, –1), (0, –2, 0), and (1, – 1, 2) is parallel to the line x=1-t,…

A: Equation of plane passing through x1, y1, x2, y2, x3, y3 is given by,…

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: Find an equation of the plane through (-8, 6, - 6) that is perpendicular to the planes 9x - y + z =…

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Q: Find the line of intersection of the planes 2x+y-z=3 and x+2y+z=2. Find the equation of the plane…

A: Solution of part (a) in step2 and step3 and part (b) in step4.

Q: 17) An equation of a plane passing through the point ( 1, -2, 3) and containing the line L: x = 3 –…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: If the image of the point (1 -2 3) in the plane 2x+3y-z=7 is the point x, y, z then the value of…

A: Let's first understand the

Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: We know that the equation of a line passing through the point a and parallel to the vector b is…

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: Perpendicular to each of the planes x – z+ y = 0 and 2x + z – 4y = 5 and containing the point (4,…

A: We have to find an equation of the plane which is perpendicular to each of the planes x-z+y=0 and…

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: 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: Find an equation of the plane. The plane that passes through the point (−3, 2, 1) and contains the…

A: It is known that equation of a plane passing through line of intersectionof planes .…

Q: Find the distances (a) Between l1 = (2+ 2t, –1+t, -3t) and l2 = (4, -5 – 3t, 1+ 4t) (b) Between the…

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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: Find an equation for the plane which contains the point P(2,1,-3) and intersection line of the…

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Q: 7 Find the Paametric equ. for the line f intersect of the Planes 3x- 6y -2z =15 and 2X+Y-22%3D5?…

A: Given two lines, 3x-6y-2z=15 ....(i) and 2x+y-2z=5....(ii) Putting z=0 in (i) and (ii) we get,…

Q: Find the equation of the plane contains the line X+1/2 = Y/3 = Z-1/4 and the line of intersection of…

A: We have given the line of intersection of planes; x + 2y - 2z = 6 , 5x - 2y - z = 0 and line; X+1/2…

Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

A:

Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: Planes as:                       2x+y-z=3x+2y+z=2;   The given point as:                        (1,…

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: 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: 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: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

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Q: Find the distance of the point (3,8,2) from the line x-1 -y+3 -z+2 measured -3 2 -4 parallel to the…

A: Given point 3, 8, 2Given line - x-12=-y+3-4=-z+2-3Let the parameters be equal to an arbitrary…

Q: The line of intersection of the planes 2x +y - z= 4 and 4x – y+3z = 2 has equation %3D O a) (x, y,…

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

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Q: The planes x + 2y + 3z = 12 and 2x + 3y + z equation is (x, y, z) = (0, 6, 0) + n(7, – 5, 1). Find…

A: Equation of a line in space :  r→ = a→ +n b→  , where…

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.