Name:________________ Vectors Day 2 Find u ∙ v and the angle between u and v to the nearest degree 1. u = 〈2, 0〉 , v = 〈1, 1〉 2. u = 〈 − 6, 6〉 , v = 〈3, 1〉 3. u = 2i + j, v = 3i – 2j 4. u = ‐5j, v = ‐i ‐ √3 j 5. u = i + j, v = i – j Determine whether the given vectors are orthogonal 6. u = 〈6, 4〉 , v = 〈 − 2, 3〉 7. u = 〈 − 2, 6〉 , v = 〈4, 2〉 8. u = 2i, v = –7j 9. u = 2i ‐8j, v = ‐12i – 3j Find the indicated quantity, assuming u = 2i + j, v = i – 3j, and w = 3i + 4j 10. u ∙ v + u ∙ w 11. u ∙ (v + w) 12. A man pushes a lawn mower with a force of 30lb exerted at an angle of 300 to the ground. Find the horizontal and vertical components of the force. 13. A river flows due south at 3mph. A swimmer attempting to cross the river heads due east swimming at 2mph relative to the water. Find the true velocity of the swimmer as a vector. 14. A Boeing 747 maintains a constant airspeed of 550mph headed due north. The jet stream is 100mph in the northeasterly direction. a. Express the velocity va of the 747 relative to the air and the velocity v w of the jet stream in terms of i and j. b. Find the velocity of the 747 relative to the ground c. Find the actual speed and direction of the 747 relative to the ground. 15. Two forces of magnitude 30 newtons (N) and 70N act on an object at angles of 450 and 1200 with th positive x‐axis as shown below. Find the direction & magnitude of the resultant force; that is, find F1 + F 2 16. A river has a constant current of 3km/hr. At what angle to a boat dock should a motorboat capable of maintaining a constant speed of 20km/hr be headed in order to reach a point directly opposite the dock? If the river is ½ km wide, how long will it take to cross?
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