# Vector Calculus Question

by spoc21
Tags: calculus, vectors
 P: 87 1. The problem statement, all variables and given/known data The displacements of two ships, A and B, two hours after leaving from the same port can be represented with position vectors $$\vec{OA}$$ [20, 50, 0] and ($$\vec{OB}$$) [60, 10, 0]. Assume that the port is located at the origin and that all units are in kilometres. a. How far from the port is each ship? b. How far apart are the two ships? These subparts are part of the same question: The displacement of a bird from the port can be described with the vector -65 i – 8 j + 0.5 k i) How high above the water is the bird? ii) How far from ship B is the bird? d. What will be the position vector of the displacement of ship A from the port 3.5 hours after leaving the port? Assume that the direction and speed of the ship are constant. 2. Relevant equations 3. The attempt at a solution For qu a, I just took the magnitude of the vectors OA, and OB, using the magnitude formula, getting 53.85 km, and 60.83 km for the distances from the port. I was just wondering if this method is correct? For b, I'm confused, would I just add the two vectors OA and OB, and then find the magnitude of the resultant vector , I'm 90% that this method is correct, but would appreciate any helpful tips. For qu c, part 1, I'm thinking that the first part is the same as a), since we just calculate the magnitude of displacement vector from the origin (but am very unsure about this) for qu c), part 2, I am very confused, and tips to help me get started would be greatly appreciated. For qu d), Im thinking that we just divide the displacement vector of ship B by 1.75, in order to get the position vector for the ship after 3.5 hours. Again, I am very unsure about this. I would really appreciate any help, thanks.