Consider the points A(1,-1, 4), B(2, –3, 2), C(-1,-2, 2), and D(4,3, -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 = (b) Find the distance fromD to the plane containing A, B, and C. NOTE: Enter the exact answer.

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

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: Consider the three vectors u = (0, -2,3), v = (1,-4,0) and w=(-4,3,-5). a) Find the cross product…

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Q: Consider the points A(3,-3, 2), B(6, -5,0), C(-1, –4,0), and D(6,3,-4). (a) Find the volume of 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: Consider the points A(3, –3, 5), B(5, –5, 2), C'(-1, –4, 2), and D(4, 1, –8). (a) Find the volume of…

A: AB→=(5, -5, 2)-(3, -3, 5)AB→=(2, -2, -3)AC→=(-1, -4, 2)-(3, -3, 5)AC→=(-4, -1, -3)AD→=(4, 1, -8)-(3,…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (4, 2, -2), b = 3…

A: Given:- a = (4, 2,-2), b = (0, 2, 1), c = (4, -3, 4) To find :- Volume of Parallelepiped

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: Find the distance (correct to two decimal places) between the given parallel planes. 4x+7y-2z=12 and…

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Q: Consider the points A(3,-3, 3), B(4, –5, 1), C(-2,-4, 1), and D(6,3,-5). (a) Find the volume of the…

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Q: Consider the points A(2, –3, 4), B(4, -5, 1), C(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of…

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Q: Find the distance between the given parallel planes. 2x+y + 2z = 8 and 4x+2y + 4z + 5 = 0

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