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1. If two vectors have the same magnitude, do their components have to be the same? 2. Explain why a vector cannot have a component greater than its own magnitude. 3. Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your position? starting point and what is the compass direction of a line connecting your starting point to your final 4. For the vectors given in the following figure, use the tip to tail method to sketch the following vector sums. Then, compute the components of each resultant vector. (a) A +B 50 (b) C +B C - 1 12.0 C 4 (c) D + F A = 10.0 (d) A - B 30 (e) D - F 30 (f) A + 2F F = 20.0 B - 5.0 (g) C - 2D + 3F 53 D (h) A - 4D + 2F D = 20.0 37 5. The magnitudes of two displacement vectors are A = 20 m and B = 6 m. What are the largest and the smallest possible values of the magnitude of the resultant R = A + B? 6. For vectors B = (-1, -4) and A = (-3, -2), calculate (a) A + B and its magnitude and direction angle, and (b) A - B and its magnitude and direction angle