Find the standard equation of the sphere. Endpoints of a diameter: (0, 0, 4), (4, 6, 0)

Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x−3y+2z=4.

Write the equation of a circle. a circle with a diameter having endpoints at (0, 4) and (6, -4)

In the following exercise, find the standard equation of the sphere with the given characteristics.

Endpoints of a diameter: (-2, 4, -5), (-4, 0, 3)

Find the standard equation of the sphere. Center: (-3, 2, 4), tangent to the yz-plane

Find the standard equation of the sphere with the given characteristics. Center: (3, -2, 6); Radius: 4

Find the standard equation of the sphere with the given characteristics. Center: (−4, 0, 0), tangent to the yz-plane

find the standard form of the equation of the sphere with the given characteristics. Endpoints of a diameter: (3, 0, 0), (0, 0, 6)

Find the points of horizontal and vertical tangency (if any) to the polar curve. r = 1 - cos θ

Let u = PQ and v = PR and (a) write u and v in component form, (b) write u and v as the linear combination of the standard unit vectors i and j (c) find the magnitudes of u and v, and (d) find 2u + v. P = (-2, -1), Q = (5, -1), R = (2, 4)

Let u = PQ and v = PR, and find (a) the component forms of u and v, (b) u·v, and (c) v·v. P = (2, -1, 3), Q = (0, 5, 1) R = (5, 5, 0)

find the coordinates of the point. The point is located three units behind the yz-plane, four units to the right of the xz-plane, and five units above the xy-plane.

find the lengths of the sides of the triangle with the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. (1, -2, -1), (3, 0, 0), (3, -6, 3)

Determine the location of a point (x, y, z) that satisfies the condition(s). x > 0