Multi variable Calculus Problem Set

1. Find two vectors vi and v2 whose sum is (-5, 1), where VI is parallel to (-1, -2) while V2 is perpendicular to (-1, -2). and 12 = . 2. Find the angle 0 between the vectors a = 10i - j - 5k and b = 2i + j -4k. Answer (in radians): 0 =. 3. Find a vector a that has the same direction as (-8,9,8) but has length 4. Answer: a =. 4. A boat is heading due east at 29 km/hr (relative to the water). The current is moving toward the southwest at 9 km/hr. (1) Give the vector representing the actual movement of the boat. (2) How fast is the boat moving, relative to the ground? km/hr. (3) By what angle does the current push the boat off its due east course? Your answer should be a positive angle less than x radians