91Ó°ÊÓ

Find the unit vector in the direction of the given vector. $$ \mathbf{v}=\langle-9,-12\rangle $$

A car that weighs 2500 pounds is parked on a hill in San Francisco with a slant of \(40^{\circ}\) from the horizontal. How much force will keep it from rolling down the hill? Round to the nearest pound.

Express the vector as a sum of unit vectors \(i\) and \(\mathbf{j}\). $$ \langle 5,-3\rangle $$

In Exercises 59-62, determine whether each statement is true or false. The Law of Sines applies only to right triangles.

How much work is required to push a lawn mower 100 feet if the force applied to the handle is 70 pounds and the handle makes an angle of \(40^{\circ}\) with the horizontal? Round to the nearest ft-lb.

Express the vector as a sum of unit vectors \(i\) and \(\mathbf{j}\). $$ \langle 0,2\rangle $$

In Exercises 63-66, determine whether each statement is true or false. Orthogonal vectors have a dot product equal to zero.

A force of 630 pounds is needed to pull a speedboat and its trailer up a ramp that has an incline of \(13^{\circ}\). What is the combined weight of the boat and its trailer to the nearest pound?

A ship's captain sets a course due west at \(12 \mathrm{mph}\). The water is moving at \(3 \mathrm{mph}\) due north. What is the actual velocity of the ship, and in what direction is it traveling?