Convert the point from rectangular coordinates to spherical coordinates.  

Find an equation of a plane passing through the points and perpendicular to the plane.  

Find the component form of the vector u with the given initial and terminal points. Initial point: (2, 1, 1 ) Terminal point: (7 , 10 , 3 )  

Complete the square to write the following equation in the standard form for a sphere. ​ ​

Given and , find the vector component of u orthogonal to v. ​

Find the vector v whose initial and terminal points are given below. (6,2), (2,–2)  

Given , find .  

Find the distance between the planes given below.  

Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point where . Also, at time t, the second insect is at the point where . Assume distances are given in inches. Find the distance between the two insects at time . Round your answer to two decimal places.  

Given and , find . ​