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13. u = 2i + 3j, v = -i - 2j 14. Find a unit vector in the direction of v = 7i + 4j.
13. u = 2i + 3j, v = -i - 2j 14. Find a unit vector in the direction of v = 7i + 4j. 15. Find the component form of the vector v with ||v|| = 12, in the same direction as u = (3, -5). 16. Forces with magnitudes of 250 pounds and 130 pounds act on an object at angles of 450 and -60, respectively, with the positive x-axis. Find the direction and magnitude of the resultant of these forces. 17. Find the dot product of u = (-9, 4) and v = (1, 3). 18. Find the angle between the vectors u = 7i + 2j and v = -4j. 19. Are the vectors u = (6, -4) and v = (2, -3) orthogonal? Explain. 20. Find the projection of u = (6, 7) onto v = (-5, -1). Then write u as the sum of two orthogonal vectors. 21. Write the complex number z = -2 + 2/ in trigonometric form. 22. Write the complex number 100(cos 240 + i sin 2409) in standard form. In Exercises 23 and 24, use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form. 23. 3( cos Sur + i sin So) 24. (3 - 3i)6 25. Find the fourth roots of 128(1 +
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