Find the point of the intersection of the plane P: 2x- 3y + 4z + 14 = | 0 and the line L:x =1-t, y = 1+t, z= 2 + 3t

Q: Find the point at which the line intersects the given plane. x = 4 − t,  y = 2 + t,  z = 3t;    x −…

A: x = 4 − t,  y = 2 + t,  z = 3t;    x − y + 5z = 15 We need to find the point at which the line…

Q: Find the distance between the point (1, 0, 2) and the plane 2x – 3y + 6z = 6.

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Q: Find the plane determined by the intersecting lines. z = 1-t L1 x= - 1 +t y = 2 + 3t L2 x = 1- 4s y…

A: Given: L1  x=-1+t    y= 2+3t   z=1-tL2  x=1-4s   y=1+2s   z=2-2s To find equation of  plane by these…

Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z12 20. (2,8,4) and 2x+…

A: a) given point is (0,0,0)  plane is 2x+3y+z=12 find the distance between the point and the plane  b)…

Q: Find the angle of intersection of the plane 2x+3y+5z=−32x+3y+5z=−3 with the plane 3x+2y−1z=0

A: Given: - The plane is, 2x+3y+5x=-3, with the plane 3x+2y-z=0 To find: - The angle of intersection of…

Q: Locate the point of intersection of the plane 2x + y−z = 0 and the line through (3, 1, 0) that is…

A: Our Aim is to locate the point of intersection of the plane 2x+y-z and theline through (3,1,0) that…

Q: Choose the line which is completely on the plane 2x+3y-4z= 12. Select one: x-1+3t, y= 1+3t, z 2+2t,…

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Q: Find the distance between the point (3,4,5) and the plane 2x + 4y 3z = 12.

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Q: find the point (x, y, z) where the line of intersection of the plane a: x-2y + 4z = 0 and the plane…

A: Find the ,line then point on the plane.

Q: (6) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane r+y+ z = 6?

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

A: given planes are x+y-z = 5, 4x-y+5z = 1 The equation of plane that contains intersection of planes…

Q: Find an equation of the plane passing through (0,-2,3) that is orthogonal to the planes 2x+ 2y-5z 0…

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Q: Find the distance of the point (3,8,2) from the line , -y+3 -z+2 Q2: measured parallel to the plane…

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Q: Find the distance between the point (1, 3, −1) and the plane 3x − 4y + 5z = 6.

A: According to the question, we have to find the distance between the points 1,3,-1and the plane…

Q: Is the line x = 4 + 2t, y =-t , z=-4t - 1 parallel to the plane 3x + 2y + z = 7 ?

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Q: What is the intersection of the plane x+2y+z =0 and the line (x, y,z) = (0,1,2)+ k(–1,1,2), kER?

A: Consider the equation of plane x+2y+z=0 and the equation of line x,y,z=0,1,2+k-1,1,2. Find the…

Q: Find the distance between the point (0, 1, 2) and the plane 3x - 2y + 6z = 6.

A: Using Distance from point to plane formula,

Q: Find the distance from the plane given by 6x − 2y + 3z − 1 = 0 to the point (4, 1, 3).

A: The distance from plane to a point is given by  d=Ax1+By1+Cz1+DA2+B2+C2 Where Plane is Ax+By+Cz+D=0…

Q: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

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Q: The lineL: x = 3 + 2t, y = 2t, z = tintersects the plane x + 3y - z = -4 in a point P. Find the…

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Q: Find an equation of the plane whose points are equidistant from (6, -5, 3) and (7,5, 5). 13x + 8z –…

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

A: Please see the explanation below

Q: Determine the intersection of the perpendicular line drawn from the point A (-5, 3, 7) to the plane…

A: The equation of the plane is given as, v=0,0,2+t1,1,3+s2,0,-3 Or…

Q: Find the general equation of the plane containing the point (2,-1,4) and normal to the line 2 I+3…

A: The equation of the line passing through the points x1,y1,z1 with direction ratios a, b and c is…

Q: Locate the point of intersection of the plane 2x + y - z = 0 and the line through (4,2,0) that is…

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Q: Find an equation of a plane passing through the points (1, –1, 7), (3, 2, –20) and perpendicular to…

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Q: Find the distance between the point P(1, -2, 2) and the plane 2x + 3y + 6z - 1 = 0.

A: Formula to find out distance between point and plane is D= |ax+by+cz-d|/√(a^2+b^2+c^2)

Q: Find an equation of the plane passing through (0,-1,3) that is orthogonal to the planes 3x+4y-2z=0…

A: Let's find equation of the plane.

Q: Find an equation of the plane through (-2, 8, – 5) that is perpendicular to the planes 2x – y + z =…

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Q: int at which the line ⟨4,−1,−5⟩+t⟨−3,3,2⟩⟨4,−1,−5⟩+t⟨−3,3,2⟩ intersects the plane…

A: Given the line 4,-1,-5+t-3,3,2  intersects the plane -x+y+z=18.

Q: Find the distance between the point (2, 0, 1) and the plane 2x - 3y + 6z = 6.

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Q: Find the equation of the plane that contains both of the lines given below. Line 1: x = 1+t, y = 2+…

A: Line 1 : x=1+t, y=2+2t, z=3-t        ⇒a⇀=1, 2, 3, l⇀=1, 2, -1 Line 2 : x=1-s, y=2+4s, z=3+2s…

Q: Derermine the pointof intersection of the linel:- [-6,9,-1]+t[-a,3 ,1], t ER, and the plane, TT-x +…

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Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…

A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…

Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

Q: Find an equation of plane through the points pl (-1, 1, 1) and point of intersection of the plane 2x…

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Q: Determine the distance from point Q = (2, 6, 9) to the plane x + 2y + 2z = 8

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Q: Find an equation of the plane passing through (0,−3,1) that is orthogonal to the planes 5x+5y−4z=0…

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Q: Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…

Q: What is the distance between the point A(1,-1,3) and the plane x + 2y + 2z + 1=0 ?

A: To find The diatance between the point A(1,-1,3) and the given plane

Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line WWWw…

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

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Q: between the point and the plane. 43. (1,−2, 3); 2x − 2y + z = 4

A: Given: The point is 1,-2, 3 and the equation of the plane is 2x-2y+z=4 To find the distance between…

Q: 4. Find the point of intersection of the plane z= 4 and the line L={ (x, y, z) | x= 4 + 3t, y=-1-2t,…

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Q: What is the intersection of the plane x+2y+z=0 and the line (x,y,z) = (0,1,2)+ k(-1,1,2), kER?…

A: hello greetings from bartelby.i am here to help you.

Q: Find the point of intersection of the lines x t, y = -t + 2, z = t + 1, and x 2s + 2, y s + 3, z 5s…

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Q: Find the distance between the point (1, 0, 2) and the plane 2x − 3y + 6z = 6.

A: To find the distance

Q: Find a plane containing the point (3,-7,8) and the tine of intersection of the planes-4z +4y + 4z =…

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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.