Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y = 3 +t z = -2+3t

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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 .

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Q: Find the point where the line x = 8/3+ 2t, y = -2t, z = 1 + t intersects the plane 3x + 2y + 6z = 6.

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Q: Find an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…

A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…

Q: Find an equation of the plane that contains the line l(t) =(-1,1,2)+t(3,2,4)y which is perpendicular…

A: As given by the question There are given that the equation of line: lt=-1, 1, 2+t3, 2, 4 And, The…

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A: topic - equation of plane

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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 Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

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Q: Find an equation of the plane that is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

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Q: Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets…

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Q: Find the equation of the plane that contains point P1(1,0,3) and orthogonal to line L1:(5t – 1,3 –…

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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 point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

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Q: Find an equation of the plane that contains the point (2, 0, 3) and the line x =-1+t, y =t, z=-4+21…

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Q: Find an equation of the plane that is parallel to the y-z plane and that passes through the point…

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Q: Find an equation of the plane that contains the line x = −2 + 3t , y = 4 + 2t , z = 3 −t and is…

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Q: Find the equation of a plane through the point(- 3, – 2, 3) and orthogonal to the line x(t) - 5+ 8t…

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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…

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

A: Here the two equation are: x+2y+z=1x+y+2z=-1

Q: 4. Find the equation of the plane that contains the intersecting lines a = 4 +t1, y = 2t1, z =1-3t…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Give the general equation of the plane containing the point (3,-1,4) and x 2-2 perpendicular to the…

A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

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Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is  x+2y-10z+12=0 We need to find the equation of plane that is…

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Q: Find an equation of a plane containing the line r=⟨0,−5,−1⟩+t⟨−2,4,−2⟩ which is parallel to the…

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Q: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

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

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Q: Find an equation of the plane. The plane that passes through the point (2, 4, 5) and contains the…

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Q: The equation of the plane passing through the point A(4, 9, 4) and orthogonal to the line a = 9 +…

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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…