Find an equation of the plane. The plane that passes through the point (1, 2, 4) and contains the line = 4t, y = 1+ t, z = 2 -t Зх -9у + 3z%3D -6 а. b. 3x - 9y + 3z = 3 3x +9y + 3z = - 3 с. d. 3x +9y +3z = - 6 е. 3x - 9y + 3z = - 3

Q: Find an equation of the plane that is parallel to the plane x + 8y – 4z + 12 = 0 and contains the…

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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: Find the equation of the plane passing through the points (1,0, -1), (-1,2,1) and parallel to the…

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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…

A: At the point of intersection the point will satisfy the equation of both line and the plane. So…

Q: Find an equation of the plane determined by the point P(1,1,3) and the line given by (x-2)/3 =…

A: Given that: x-23=y+14=z-42 and P(1, 1, 3)

Q: Find an equation of the plane determined by the points P(1,2,3), Q(2,0, 1), and R(0, –-1,1).

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Q: Find an equation of a plane that passes through the points P(1,2,-2), Q(-2,1,4), R(2,1,1) a.…

A: As we know that; The determinant form to calculate the equation of the plane when it passes through…

Q: Find an equation of the plane that is parallel to the plane x + 4y – 3z + 16 = 0 and contains the…

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Q: Find the equation of the plane that contains the point P(3,5,-1) and the linex = 4 - ty = -1 + 2t,z…

A: The plane contains the point P(3,5,-1) and the line x=4-t, y=-1+2t, z=-3t

Q: Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

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Q: Determine the general equation of the plane containing the point (1, 2, –1) and the line

A: The given equation of the line- 1-x3=y+23=z-3 It can also be written as follows- x-1-3=y+23=z-31…

Q: Find an equation of a plane that passes through the points P(4,2,1), Q(-1,-2,2), R(3,1,-2) a.…

A: A plane that passes through the points P(4,2,1), Q(-1,-2,2), R(3,1,-2)

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: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: find the equation of the plane passing through(1,0,-1)&(-1,2,1) and parallel to the line of…

A: To determine: The equation of the plane passing through the points (1, 0, -1) and (-1, 2, 1) and…

Q: Determine the equation of the plane passing through the points P(-2, 1, 5) and Q(4,9, -3) and R(3,…

A: To determine the equation of the plane passing through the points P(-2, 1, 5) and Q(4, 9, -3), and…

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

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Q: Determine the equation of the plane that passes through (2,-4,1) and is perpendicular to the line of…

A: A plane is passing through 2, -4,1 and perpendicular to the line of intersection of the plane  3x -…

Q: Find an equation of a plane passing through the points (1, –3, –59), (–3, 2, 54) and perpendicular…

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Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

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

A: This question can be solved using the concept of planes in three dimensional geometry.

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 linear equation of the plane through the point (1, 7, 6) and parallel to the plane x + 3y +…

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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: Determine the equation of the plane that contains the points P(1,−2,0), Q(3,1,4) and R(0,1, -2)

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Q: Find the intersection of the line r(t) = (2, 1, 3) + t(3, -3, 1) and the plane 4x - 4y - 2z = 6.

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

Q: Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x – y + z = 2…

A: For solving This question I found direction cosine using dot product as two perpendicular plane is…

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

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Q: Find the point at which the line intersects the given plane: 5x = y/2 = z + 2 and 10x - 7y + 3z +…

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

A: Here we use elimination process.

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: Find the point at which the line (-4, –5, 2) + t(-4, 3, –5) intersects the plane 2x + 5y + 4z = -6

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Q: Find the equation of the plane that passes through the points A = (1, –4, –1), В - (-5, —3, —5), and…

A: Proceed as shown below

Q: Find a plane containing the point (-4,-7,3) and the line of intersection of the planes - 2x + 7y +…

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

A: Given,            The plane passes the point -3, 3, 3 and also contains the line of intersection of…

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z…

A: To Find : Equation of plane passing through (-3,8,-8) that is perpendicular to the plane7x-y+z=2 and…

Q: Find a plane containing the point (5,8,8) and the line of intersection of the planes -4x 4y+ 6z = 74…

A: We have to find the equation of plane containing the points 5,8,8 and the line of intersection of…

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

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

Q: Determine the equation of the plane that contains the points P=(1,-2,0) P=(1,-2,0), Q=(3,1,4)…

A: Here we have to determine the equation of the plane that contains the points P(1,-2,0), Q(3,1,4) and…

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: Determine the general form of the equation of the plane passing through P(2,1,-1), Q(0,-2,0) and…

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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 the equation of the plane that passes through the point (1,0,-2) and contains the line with…

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Q: find the equation of the plane passing through (1,0,-1)&(-1,2,1) and parallel to the line of…

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Q: 4] Find the equation of the plane that contains the point (a, 0, 0), (0, b, 0) and (0,0, c).

A: As per our company guidelines we are supposed to answer only one question kindly post other parts in…

Q: Find an equation of the plane that is parallel to the plane x + 2y – 7z + 15 = 0 and contains the…

A: A detailed solution is given below.

Q: What is the equation of the plane containing the points (4,−3,1), (−3,−1,1) and (4,−2,8)? A. 14x…

A: Solve by eq

Q: of the

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Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…