817 8.4 Algebraically Defined Vectors and the Dot Product Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary. See Example 1. 9. 85, 79 10. 8-4, -79 11. 815, -89 12. 8-7, 249 13. 8-4, 4239 14. 8822, -8229 8.4 Exercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. The magnitude of vector u is . 2. The direction angle of vector u is . 3. The horizontal component, a, of vector v is . 4. The vertical component, b, of vector v is . 5. The sum of the vectors u = 8-3, 59 and v = 87, 49 is u + v = . 6. The vector u = 84, -29 is written in i, j form as . 7. The formula for the dot product of the two vectors u = 8a, b9 and v = 8c, d9 is u # v = . 8. If the dot product of two vectors is a positive number, then the angle between them is . (acute / obtuse) y x 1 u u = 〈√3, 1〉 0 u Ë3 y x b a 1 458 v 0 Vector v has the given direction angle and magnitude. Find the horizontal and vertical components. See Example 2. 15. u = 20°, v = 50 16. u = 50°, v = 26 17. u = 35° 50′, v = 47.8 18. u = 27° 30′, v = 15.4 19. u = 128.5°, v = 198 20. u = 146.3°, v = 238 Write each vector in the form 8a, b9. Write answers using exact values or to four decimal places, as appropriate. See Example 3. 21. y x u 5 0 308 22. y x u 8 608 0 23. v 4 1408 x y 0
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