Determine the relative position of the following planes. If applicable, describe the intersection using a vectorial description (specifying whether it is a straight line or a plane). (a) Π1: 3x−y+ 2z= 5, Π2: 2x+ 2y+z= 4 and Π3: 3x−3y+z= 2. (b) Π1: 3x−y+ 2z= 5, Π2: 2x+ 2y+z= 4 and Π4: 4x−4y+ 3z= 6.

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A: Given the equation of planes, x+2y-2z=14x-y+2z=7

Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

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Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

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A: A plane in ℝ3 is perpendicular to the vector 4, 2, -9 and contains point -9, 5, -8To find the…

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Q: Determine the Cartesian equation of a plane that has x-, y-, and z- intercepts 1/3, 1, and -1/2,…

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Q: III. Consider the line ₁ given by the symmetric equations +1=-y-1 B 2 and the line ₂ given by the…

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Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

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Q: B 10. Write a vector equation and parametric equations for a plane that satisfies each set of…

A: Due to Bartleby answering guidelines I have solved only first three Subparts of the given question…

Q: - a) Determine the vector equation of the line of intersection of these 2 (1) x + 2y + 2z = -3 (2 2x…

A: Note:  part(b) is the independent subpart of part(a) and also it is incomplete. so part (b) can't be…

Q: 2. Write the plane equation when it passes through a point Mo(11,2) and is: a) perpendicular to the…

A: We have to find the equation of the plane.

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Q: Consider a plane with direction vectors  [−2,8,5] and  [5,0,−7]. The plane passes through the point…

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