Exam 11: Three-Dimensional Space; Vectors

What is the radius of the sphere

Identify the trace of the surface defined by when .

Find the parametric equations for the line passing through and .

If , , and , find and .

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

If , then find

The graph of is an infinitely long cylinder whose central axis is the

Identify the quadratic surface defined by .

Identify the quadratic surface defined by .

Find the dot product.

What is the radius of the sphere

Convert (1, 1, 10) from rectangular to cylindrical coordinates. Coordinates are written as .

Determine if the three vectors <2, -2, 1>, <1, -4, 1>, and <4, -4, 2> are coplanar.

Find the dot product .

Let . Find the length of u.

What is the volume of the parallelopiped that has u = <2, 5, -3>, v = <1, 10, 1>, and w = <-3, 10, 2> as edges?

Find the equation of the sphere with a diameter whose endpoints are and .

Find the dot product .

Find the angle between and . Round the angle to one decimal place.

Convert from spherical to cylindrical coordinates.