Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis and by the lines y=x and x= 1, the top of which is in the z= 2 - y plane. 2 z= 2 - y y =x

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

A:

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: Use the applet to translate quadrilateral ABCD 2 units left to create quadrilateral A'B'C'D', then…

A:

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (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: ind the equation of the tongent plane to fox,y)=x²-2xy + 2y ² slope 2 in the positive x direction…

A:

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+ 2y+ 2z = 13 2. Find the distance from…

A:

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

A:

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

A:

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: Suppose C is the triangle with vertices (3, 0, 0), (0, 4, 0), and (0, 0, 1) oriented…

A:

Q: Let T be the plane -y+2z = 7. Find the shortest distance d from the point Po=(2, 3, −4) to T, and…

A:

Q: c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

A:

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

A:

Q: 1. Find the plane which contains the point M (4, 5,0) and the line 2+3 = ¹ = 2²

A: To find the plane which contains the point M4, 5, 0 and the line x+35=y-4-3=z-22.

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Two planes are perpendicular iff their normal vectors are orthogonal

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.