The equation of the plane passing through the point A(4, 9, 4) and orthogonal to the line a = 9 + 8t, y = 7+ 5t, z = 2 + 2t is given by

Q: Find an equation of a plane containing the line r = (2, –2, 3) + t(12, –8, 4) which is parallel to…

A: Equation of plane parallel to the plane 4x+4y-4z=-17 is of the form  4x+4y-4z=k This plane contains…

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 an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: Find the equation of the plane through the point (2,4,3)(2,4,3) that is perpendicular to the line…

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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 an equation of a plane containing the line r = (4, –5, –4) + t (–7, 8, –4) which is parallel to…

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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 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…

Q: Find the equation of the plane for a plane through the point (2, −8, −3) and parallel to the plane…

A: Equation of plane through point (x1, y1 , z1) and parallel to plane ax +by+cz+d = 0 is given as…

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

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Q: Find the equation of the plane that contains the line x=-1+3t, y=5+2t, z=2-t and is perpendicular to…

A: topic - equation of plane

Q: Find the symmetrical point of point P(-1,-3,5) with respect to the plane D:3x-2y+z+6=0

A: Point P(-1,-3,5)  plane D:3x-2y+z+6=0

Q: The equation of the plane passing through the point A(6, 6, 6) and orthogonal to the line a = 11 +…

A: The objective is to find the equation of the plane passing through the point A6,6,6 and orthogonal…

Q: Find the equation of the plane through the point P = (2, 5, 4) and parallel to the plane 5x – 5y +…

A: Equation of plane parallel to 5x -5y +3z = 6  is given by; 5x -5y +3z + λ  = 6 Also it passes…

Q: find the equation of the plane through P(1, 3, 2) that is parallel to the plane 5x - 4y + 3z = 7

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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 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 is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

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Q: Determine the general equation of the plane Ω passing through the point P(1,−4,−5) and parallel to…

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

A: Consider the line L1given by the vector form: L1:5t-1, 3-2t, t    :-1+5t, 3-2t, 0+t    :-1, 3, 0+5t,…

Q: Determine the general equation of the plane N passing through the point P(3, –1,2) and parallel to…

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Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

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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: Find the equation of the plane that contains the point (4, 0, −2) and is perpendicular to the planes…

A: The equation of the plane passing through the point x0, y0, z0 is given as…

Q: Find the equation of the plane containing the point P(-2,4,3) and the line y+1 z+2 %3D 4 2 -3

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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 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: The equation of the plane passing through the point A(6, 6, 6) and orthogonal to the line a 11+7t, y…

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Q: Find the equation of a plane that passes through the origin and contains the line x = 2t, y = 3t, z…

A: Consider the provided question, The equation of a plane passing through the point (x1, y1, z1) is…

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

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Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

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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 an equation of the plane in standard form (ax + by + cz = d) that passes through the point (4,…

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Q: 2. Find an equation of the plane determined by the points P(1,1,0), Q(1,0,1) and R(0, 1, 1).

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

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Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: 2) Find the equation of the plane that is orthogonal to the planes 3x-2y-2z=1 and x-3y-10z = 4 and…

A: Given: The equation of two planes 3x-2y-2z=1 and x-3y-10z=4 and the equation of one line…

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 an equation of the plane that passes through the point (1,2,3) and which is orthogonal to the…

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Q: ) Find the equation of the plane passes through the point P(2, 2, 3) and perpendicular to the two…

A: To find the equation of the plane that passes through the point P (2, 2, 3) and perpendicular to the…

Q: Find the equation of the plane through P(2, – 1,1) that is parallel to Il: 2x + 3y + z – 12 = 0. %3D

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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…

Q: Find an equation of the plane that passes through the point (1,1,2) and contains the line x=3t, y=1,…

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

A: Your line, perpendicular to the plane will have the slope of <2, -1, -1>, and passes through…

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 the point at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t   -1and plane , x+2y-z=6

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

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