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 parallelepiped that has the vectors AB, AC, and AD as adjacent edges. NOTE: Enter the exact answer. Volume 166 (b) Find the distance from D to the plane containing A, B, and C. NOTE: Enter the exact answer. 166 Distance /269

Q: Find the area of the parallelogram that has the vectors as adjacent sides. AB= 6i + 6j - 6k, AD = 6i…

A: NOTE: Refresh your page if you can't see any equations. . given vectors are find the cross product

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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: 1. Find the area of the triangle in the R2 plane whose vertices are given by (0,0), (–1,4) and (7,…

A: 1. The Area of triangle with vertices (x1,y1),(x2,y2),(X3,y3) is given by formula : ∆…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 3i + 3j − 4k, b…

A: Given that the vectors a=3i+3j-4kb=2i-2j+4kc=-4i+4j+3k     .

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

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Q: 1. Find the equation of the plane. the points. Don't use three (1,2,1), (2,6,3), (0, 1,-1) which…

A: 1:  2: Note: We have taken d as common and taken  it to the other side of the equation.

Q: If the position vectors of the points A, B, C, D are a = i +j+k, b = 2i+ 3j, c = 3i+ 5j – 2k, d= k –…

A: The position vectors of points A, B, C and D are a=i+j+k,  b=2i+3j,  c=3i+5j-2k  &  d=k-j. Now…

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: 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: 4. If the position vectors of the three points A, B and C are (2, 4, -1), (1, 2, -3) and (3, 1, 2)…

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Q: 4. Find an equation of the plane that passes through the points P(1,3,2), Q(3,–1,6), and R(5,2,0).…

A: Given points P1,3,2, Q3,-1,6, R5,2,0

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: In a three-dimensional space we have a vector R=( 4ai + 3aj + 5ak). Another vector S has the same Y…

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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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