Questions from General Calculus

Q: Invasive species often display a wave of advance as they colonize new

Invasive species often display a wave of advance as they colonize new areas. Mathematical models based on random dispersal and reproduction have demonstrated that the speed with which such waves move...

Q: Find the scalar and vector projections of b onto a.

Find the scalar and vector projections of b onto a. a = 3i - 3j + k, b = 2i + 4j - k

Q: Find the scalar and vector projections of b onto a.

Find the scalar and vector projections of b onto a. a = i + 2j + 3k, b = 5i - k

Q: Show that the vector ortha b = b - proja b is

Show that the vector ortha b = b - proja b is orthogonal to a. (It is called an orthogonal projection of b.)

Q: For the vectors in Exercise 40, find ortha b and illustrate

For the vectors in Exercise 40, find ortha b and illustrate by drawing the vectors a, b, proja b, and ortha b. Exercise 40: Find the scalar and vector projections of b onto a. a = 1, 4 , b = 2, 3...

Q: Suppose that a and b are nonzero vectors. (a

Suppose that a and b are nonzero vectors. (a). Under what circumstances is compa b − compb a? (b). Under what circumstances is proja b − projb a?

Q: Find a ∙ b. a = 4, 1

Find a ∙ b. a = 4, 1, 1 4 , b = 6, −3, −8

Q: A tow truck drags a stalled car along a road. The

A tow truck drags a stalled car along a road. The chain makes an angle of 30° with the road and the tension in the chain is 1500 N. How much work is done by the truck in pulling the car 1 km?

Q: A sled is pulled along a level path through snow by a

A sled is pulled along a level path through snow by a rope. A 30-lb force acting at an angle of 40° above the horizontal moves the sled 80 ft. Find the work done by the force.

Q: A boat sails south with the help of a wind blowing in

A boat sails south with the help of a wind blowing in the direction S36°E with magnitude 400 lb. Find the work done by the wind as the boat moves 120 ft.