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 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: 5) Flights 104 and 217 are both approaching Norfolk International Airport from opposite directions…

A: Given, Flights 104 and 217 are both approaching Norfolk International Airport from opposite…

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…

A:

Q: 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…

A: Let's find.

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: 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: Find the distance from the point P(-1,3,-5) to the plane through the three points Q(3, 1, -3). R(4,…

A: The points passing through the plane are: Q3, 1, -3R4, 6, -5S5, -4, -6

Q: Let P be the parallelogram in the plane with vertices (0,0), (1,2), (1, 1), and (2, 3). Find SSp¤…

A: We need to find integral.

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

A: Explained below

Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…