Consider the points A(3,-3, 3), B(4, -5,0), C(-3,-4,0), and D(6, 2, -6). (a) Find the volume of the parallelepiped that has the vectors AB, AC, and AD as adjacent edges. NOTE: Enter the exact answer. Volume 69 (b) Find the distance from D to the plane containing A, B, and NOTE: Emter the exact answer. 231 Distance

Q: .Find the equation and sketch the plane that contains the points (2, 6, 1), (-4, 9, -1) and (4, 3,…

A: Equation of plane is 3x+2y+6z = 12

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Q: Find an equation of the plane that passes through (2, –1, 5) and is parallel to the plane containing…

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Q: Suppose a plane through three points A(1,-2,4), B(1,-1,6) and  C(2,0,5). Solve the following two…

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Q: Given the points P (1, 2, 2), Q (2, -1, 4), R (3, 5, -2) and S(0,-1,3). (a) Use vectors to calculate…

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Q: Find the equation of the plane parallel to the line r = 2i + t(−4i + 3j + 8k) and containing the…

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Q: -) Find the distance between the point and the plane. (0, 0,0) a. + Z = 28 4x +7y+z = 28 b. Verify…

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Q: - Using the parallelogram in Problem 44 as a base, cre- ate a parallelopiped with side P, P; where…

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Q: Find an equation of the plane passing through the three points given P = (2,4, 2), Q = (4, 10, 10),…

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Q: b. A plane is uniquely determined by one point on the plane and two non-parallel vectors that are…

A: I have solved the question. Please go through that.

Q: Prove that three points P(5,-4), Q(-3,8) and R(1,2) on the rectangular coordinate plane are…

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Q: Give v that is perpendicular to a plane containing (1,2,3), (3, 4, 1) and (-1, -2, -3). Check if…

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Q: You are given the following points: A=(−4,20,16)A=(−4,20,16), B=(20,0,7)B=(20,0,7),…

A: Given- (x,y,z) coordinates of three points :A =(-4,20,16) B=(20,0,7) C=(8,-15,-19) to find- closest…

Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

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Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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Q: What is the volume of the parallelepiped determined by the vectors ⟨0,1,4⟩,⟨1,1,1⟩, and ⟨2,0,3⟩?

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Q: Given the two vectors a = i-2j+3k and b = 3i-2j+3k, Find the area of the parallelogram whose…

A: The vector a is given as a = i-2j+3k. The vector b is given as b = 3i-2j+3k.

Q: If a = (2, –1, 2) and b = (3, 2, 1), answer the following. Vectors can be entered using either or…

A: Given a=2,-1,2 and b=3,2,1