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

Q: plane intersects the triangular prism below through points A, B, and C. B.

A: When a pane intersects a prism and is parallel to the bases of the prism, the…

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: Here we have  to use the concept of vector

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

A:

Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (0, 0), (a, 0), (a /…

A: Given that vertices= (0, 0), (a, 0), (a / 2, b)

Q: Evaluate | x? zdS, where S is the part of the plane z = 2 + 4x + y above the rectangle [0, 4] × [0,…

A: To evaluate: ∫∫Sx2z dS where S is the part of the plane z=2+4x+yabove the rectangle region…

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…

A: Let's find.

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

A:

Q: a) Find the area of ​​a rosette petal given by r = 3cos3θ b) Find the equation of the plane that…

A:

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

A: Please comment if you need any clarification. If you find my answer useful please put thumbs…

Q: 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…

A:

Q: Prove that the centroid of a parallelogram is the point of intersection of the diagonals of the…

A: The vertices of the parallelogram are (0, 0), (0, a), (b, c), and (b, a + c)

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: Let a,b,c and d are position vectors of point A,B,C and D resp. Therefore a=i-3j+4k b=2i-5j+2k,…

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: Determine whether the planes are parallel, orthogonal, or neither. 2x − 10y − 2z = 6 3x − 15y − 3z…

A:

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

A: We have to find the volume of parallelepiped.

Q: Q2/ Find the area of the parallelogram of the plane of P(0,-2,3), Q(-1 , 2, 1) and C(3,3,0) where P…

A:

Q: 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…

A:

Q: Z • W Y. T. U. 10. What is the intersection of the two planes? 11. Are points T, Z, U, and W…

A: To answer the given questions using the given figure.

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: We have to solve given Questions.

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: Consider the points A(1, –1, 2), B(2, –3,0), C(-1, –2,0), and D(2, 1, –1). | (a) Find the volume of…

A:

Q: 5) Find the distance from D to the plane containing A, B, and C NOTE: Enter the exact answer.…

A:

Q: Name a plane parallel to plane JDC. ***** F B fenter answer here] 2 3. 4. 6.

A: Given shape is hexagonal prism in top and bottom are congruent hexagons joined by rectangular faces…

Q: Determine whether the planes are parallel, orthogonal, or neither. 4x − 2y + z = 4 x + 6y + 8z = 1…

A: The direction ratio of the normal vector of 4x − 2y + z = 4 is (4,-2,1) The direction ratio of the…

Q: π be the plane that touches the sphere E with center C= (2,2,2) at the point A=(7,4,2).The line…

A:

Q: While the coordinate axes separate the Cartesian plane into 4 subsets (quadrants), the xy plane, z…

A: given

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:

Q: 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…

A:

Q: The plane containing Q, S, A, U appears to be parallelto the plane containing which points?a. Q, E,…

A: The Parallel Plane: The Parallel planes are two planes that do not intersect. Since, this is cuboid.…

Q: Find the distance between the parallel planes P and P2 P: 2z-y+3z - 6 0 P2 : -4x + 2y – 6z – 2 = 0…

A:

Q: A plane meets the coordinate axes in A, B, C. If the centroid of AABC is (a, b, c). Show that 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…

A:

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:

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

A: Note: According to our answering guidelines we have to answer only one question if multiple are…

Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (0, 0), (1, 0), (0,…

A:

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

A: Let's solve for volume and distance between point and plane.

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

A: Given problem:-

Q: Find the distance of point K(1,0,1) to the plane generated by the points P(2,3,1), Q(3,-1,4) and…

A: All options are wrong i am giving Right answer with complete formula and procedure for easy…

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, 2), B(2, –3,0), C(-1,-2,0), and D(2,1, –1). (a) Find the volume of the…

A: Here, the given vectors are: A(1,-1,2), B(2,-3,0), C(-1,-2,0) & D(2,1,-1) (a) Here,…

Q: Department of water Resources Eng. A.L. Fatima Kumait Al-Zubaidy Q1): Find the point (x, y, z) that…

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…

A: The answer is shown in step 2.

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:

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: 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…

A:

Q: A plane meets the coordinate axes in A, B, C. If the centroid of aAl Show that the equation of the…

A:

Q: 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…

A:

Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (0, 0), (a, 0), (0,…

A: