Chapter 11.2, Problem 54E

An airplane takes of heading east at a speed of 459 miles per hour at an angle of 15 degrees with the horizon. What are the magnitudes if the horizontal AND vertical components of the speed vector?

If a vector has direction angles alpha = pi/4 and beta = pi/3, find the third direction angle gamma.

A pilot sets his airspeed to 500 km/h on a heading of North 65 degrees East . A strong wind is blowing 55 km/h in the direction of South 40 degrees East . Draw a position diagram to illustrate the word problem. Draw a vector diagram using the vectors in the problem to illustrate a vector representing the ground speed relative to earth.Determine the ground speed (to one decimal place) and the direction of the airplane relative to the ground (to the nearest whole degree). State the direction using quadrant bearings.

Find the magnitude and direction angle of a vector. Find the magnitude and direction angle of the vector (-4,3). Use an algebraic method and approximate exact answers with a calcular when appropriate.

1. Find a unit vector that has the same direction as the vector (-4, 2, 4). 2. What is the angle between the vector 8i + 6j and the positive direction of the x-axis?

If two nonzero vectors are perpendicular, then the angle between them is 90°. Also, the cosine of 90° is always zero. What does this tell us about the dot product of two perpendicular vectors? Explain.

A force of 6 pounds acts in the direction of 40° to the horizontal. The force moves an object along a straight line from the point (5, 9) to the point (8, 20), with the distance measured in feet. Find the work done by the force

I need help with two and three please

The current in a river is pushing a boat in direction 24 degree north of east with a speed of 16 km/hr. The wind is pushing the same boat in a direction 81 degree south of east with a speed of 7 km/hr. Find the velocity vector of the boat's engine (relative to the water) if the boat actually moves due east at a speed of 50 km/hr relative to the ground. Find the engine speed to push the boat and its direction.