Exam 12: Vectors and Matrices

Simplify the following:

Given and , does ?

Let the student vector be the number of ninth, tenth, eleventh, and twelfth graders in a high school. If the number of students in each grade increases by 5%, what is the new student vector ? Round to the nearest whole number.

A kite on a 28 meter string is flying with an angle of with the ground. What is the magnitude and the direction of the vector from the kite to the ground.

Given that and , let , where . What is ?

Let and . Find a vector of length 6 pointing in the opposite direction of .

Let the x-axis point east, the y-axis point north, and the z-axis point upward, and let the unit vectors be in kilometers. What does the vector represent?

A country has two main political parties. The vector gives the number of people who are members of the first party, the second party, and neither party, respectively. Suppose . Let be the population vector (in tens of thousands) in the year 2005. What is ?

If . Find such that is parallel to .

Let . Find

Let and . Write the displacement vector in component form.

Jack and Jill begin walking away from a water well. Jill walks 6 meters west, and then 3 meters north. When Jill stops, Jack is three times as far from the well as she is, but in the opposite direction. If is the vector pointing from Jack to the well, find the length and direction of .

The figure below shows the vector .

The vectors and are parallel.

A boat in the ocean at point (37, 58, 0) is looking at the light on a lighthouse at point (37, 0, 21). The light house is 3 units high, and sits at the edge of a cliff above the ocean. The displacement vector between the boat and the base of the lighthouse is .

A model pyramid is built using four equilateral triangles connected to a square base. If the length of one side of the base is 19 inches, how many inches high is the pyramid? Round to 2 decimal places.

How many ft-lbs of work are done pushing a 15-lb stroller with a 25 lb toddler in it up a 60 yard hill if the slope of the hill is 20 ? Round to 1 decimal place.

A canoe can travel 16 ft/sec in still water. Suppose a river is flowing at a rate of 6 ft/sec. If the canoe is traveling downstream at an angle of with the current, what is the speed of the canoe?