Answer the answer 1-5 and show work please

Use vectors in 3 dimensions Imagine a 3-dimensional world with coordinates that are labeled with x, y, and z, as if you are in a large room with walls, a high ceiling and a floor. The edges are x, y and z with z up toward the ceiling, the flat plane floor is x-y. Starting at the origin, go along "x" 5 meters. Then go parallel to "y" 6 meters. Then go up parallel to "z" 2 meters. This point is somewhere in the room above the floor. 1. What is the vector from the origin to the point? 2. What is the magnitude of that vector? That is, what is its length? 3. What angle does it make to the floor? This would be 90-0 where 0 is the angle down from the z axis. (Hint: Use z and the length of the vector to find the angle from trigonometry. ) 4. If you dropped from that point directly down to the floor, how far would you fall? 5. How long would it take, given that falling objects accelerate at 9.8 m/s every second (9.8 m/s2)? You could round this to 10 m/s2 to make the math easier. Suggestion: A vector is an object with magnitude or "length" and direction. You would write it as a symbol such as A and represent it in numbers with its projection on coordinate axes in space. In three dimensions we would call those x, y, and z and usually xy would be the floor and "z" would be the height above the floor. For the first part, we are asking "What are the components of this vector in these three coordinates?" You could write those as three numbers like this: (11,13,17) or symbolically like this: 11x + 13y + 17z. Here those symbols like x are simply little vectors of length 1 along each axis. We call them "unit" vectors. It is a concept you might not usually see in a first physics course, but may actually help to understand what we mean by "vector" and how it may be represented by coordinates (here x, y, and z). Last modified: Wednesday, 28 August 2024, 11:29 AM