Exam 11: Section 2: Vectors and the Geometry of Space

Find a unit vector u in the direction opposite of .

Find the vector v with the magnitude and direction of .

Find the standard equation of the sphere with center at and tangent to the yz-plane.

Find the magnitude of the vector v given its initial and terminal points. Round your answer to four decimal places. Initial point: (-2, -4, -5) Terminal point: (-3, -9, -10)

Find the magnitude of the vector given below.

Find the vector , ,

Find the standard equation of the sphere with center (2, 8, 4), and radius 2.

Find the coordinates of the point that is located 4 units behind the yz-plane, 6 units to the left of xz-plane, and 4 units above the xy-plane.

Given the vector v and its initial point find the terminal point of the vector. , initial point

Find a point such that the points and are collinear.

Find the component form of the vector u with the given initial and terminal points. Initial point: (5, 7, 8 ) Terminal point: (-2 , 10 , 10 )

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

Find the distance between the points given below. (-4, 2, -3 ), ( 0, 5, 1 )

Determine all the values of c that satisfy the equation given

Given the vector v lies in the yz-plane, has magnitude 8, and makes an angle of with the positive y-axis. Find the component form of v.

Suppose the guy wire to a 100-foot tower has a tension of 500 pounds. Using the distances shown in the figure, write the component form of the vector F representing the tension in the wire. Round numerical values in your answer to the nearest integer.

Find the coordinates of the midpoint of the line segment joining the points given below. (4, 8, 4), (7, 10, 7)

Find the unit vector in the direction of u.

Find the standard equation of a sphere that has diameter with the end points given below. (3, -2, 4), (7, 12, 4)

Given , find .