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Pre Calculus Unit 7 β Vectors Unit Test REVIEW Name _______________________________________ Date _____________________ Block ____________ π¨ = < π, βπ > π― = < π, π > πΊ = < βπ, π > ππ― + ππΊ 2. 1. ππ¨ β πΊ 3. ππ¨ β ππ― 4. π¨β π― + πΊ 5. ____________ β ππ¨ = π― 6. πΊ + ___________ = ππ― 7. βπ¨β 8. βπΊβ 9. What is the Direction Angle for vector π― 10. What is the Direction Angle for vector π¨ 11. Draw a sketch of vectors A, H and S in standard position. A H S Graph each of the following on the given plane. Make sure you show your Resultant Vector 12) 2S + 2A 13) H β S 14) 2A β 3H + S 15) 2H + 2A β S Show all work and round all answers to 2 decimal places. 17. While flying due east at 120 km/h, an airplane is also carried northward at 45 km/h by the wind blowing due north. What is the planeβs resultant velocity (Speed and Direction)? 18. An airplane is traveling at a speed of 500 mph with a bearing of N40oW at a fixed altitude and no wind. As the plane crosses the Mississippi river, it encounters a wind blowing with a velocity of 50 mph in the direction of N20oE. What is the resultant speed and direction of the plane? 19. A boat traveled south across a river at 12 miles per hour. The current of the river is 5 miles per hour 20o south of west, perpendicular to the direction the boat is traveling. What is the resultant vector (speed and direction) of the boat? 20. A force of 100 lbs. makes an angle of 660 with a second force. The resultant of the two forces makes an angle of 32° with the first force. Find the magnitude of the second force and the resultant. 21. Two forces are acting on an object. The first force, F1 of 50 newtons, pulls at an angle of 400 north of due west. The second force, F2 of 25 newtons, pulls at an angle of 300 east of north. What is the magnitude and direction of the resultant force on the object? 22. Two ships leave a port at the same time. The direction of the first ship is N 73° E and the direction of the second is S 65° E. If the ships travel at the rate of 12 knots (1 knot = 1 nautical mile per hour) and 15 knots, respectively, determine how far apart they are after 2 hours 23. A 10,000 pound object is suspended on a wire tied to two poles. The angle between the horizontal and the wire to the shorter pole is 22o. The angle between the horizontal and the wire to the taller pole is 49 o. Find the tension in the cable to each pole.