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1. Given that A= 2i + 3j + K and B= i + 3j + 2k, determine the angle between A×B and the z-axis?

2. Argue that A·(A×B) = 0. In three dimensions find the expression of A×B in terms of vector components and i, j and k. 3. A rabbit and a tortoise compete in a race over a course 1.00 km long. The tortoise crawls straight and steadily at its maximum speed of 0.200 m/s toward the finish line. The rabbit runs at its maximum speed of 8.00 m/s toward the goal for 0.800 km and then stops to tease the tortoise. How close to the goal can the rabbit let the tortoise approach before resuming the race?

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