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Exam 12: Vectors and Matrices

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Question 51

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If and , then what is ?

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Question 52

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The unit vector from the point (1, 3) toward the point (3, 5) has its head at the point ( _____, _____ ). Round to 2 decimal places.

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Question 53

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A snow cone stand sells three sizes of snow cones: small, medium, and large. Let give the number of each type of cone sold in one day. Let give the price (in dollars) charged for each size of snow cone, give the cost (also in dollars) of making each size of snow cone, and give the maximum number of each size that can be sold (because of the number of each size cup on hand.) What is the total number of cups left in the stand at the end of the day?

As t changes, what happens to the tip of the vector ?

A vector of length 8 that points in the same direction as is . Give each answer to 3 decimal places.

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 ?

Let be a vector of length 3 pointing north of east. Find the length and direction of .

In the figure below, each square is 4 units along each side. In component form, .

For what value of x are and perpendicular?

Which of the following vectors are parallel to ? Mark all that apply.

Suppose a man starts at work and drives 6 km due south, and then drives 14 km southeast. How far is the man from work?

If , what is ?

Simplify

What properties of vector addition and scalar multiplication are necessary to show

Do the points (11, 8), (12, 6), (13, 7), and (13, 8) form a square?

A gun mounted on a train points vertically upward. The train moves horizontally due east at 80 mph and the gun fires a bullet with a muzzle velocity of 80 mph. The speed and direction of the bullet relative to the ground is _______ mph toward the east at ______ to the horizontal. Round the first answer to 2 decimal places.

Is the gravitational force between a satellite and the earth a vector or a scalar?

Given , , , and , does ?

A cannon is fired at a angle with the ground at a speed of 80 ft/sec. Resolve the velocity vector into horizontal and vertical components.

In the figure below, each square is 8 units along each side. The vector perpendicular to the displacement vector is .