A vector has the given initial and terminal points. What is the corresponding position vector? Initial point: \( (0,0,0) \) Terminal point: \( (-5,3,4) \) Position vector: [ Ex: 5 ,

To find the position vector, you simply subtract the coordinates of the initial point from the terminal point. So we have: \[ \text{Position vector} = \text{Terminal point} - \text{Initial point} = (-5 - 0, 3 - 0, 4 - 0) = (-5, 3, 4). \] And there you have it! The position vector is \([-5, 3, 4]\). Vectors are not just math problems though; they're used in many real-world applications! For instance, in physics, the position vector helps describe an object's location in 3D space, playing a crucial role in navigation, robotics, and computer graphics. By understanding vectors, engineers can optimize trajectories, design more efficient assembly lines, and even improve the accuracy of virtual reality environments!