5) 2z dV, E is the solid enclosed by the cone % = Vr2 + y? and the E plane z 5

Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: Find the coordinates of the point p on the plane #₁ - 2 + 2x3 = 0, that is closest to the point b =…

A: x1-x2+2x3=0  that is closest to the point (2,0,-2)

Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top…

A: We are asked to draw the isometric view of the solid.

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

A:

Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

A:

Q: Qs/ Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

A:

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the point on the plane 8x - y + 8z = 80 nearest the origin. (x, y, z) =

A:

Q: Q2) L, - X+2 +2 ー1 - 2 Frand equaton of plane Coudentg

A:

Q: Q3/ The distance between the plane 2x+4y-4z-22%-0 and the point(1,-2.2) will be ?

A: Basic 3d geometry problem

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.