When discussing the addition of two vectors, the goal is often to determine the resulting vector's direction and size. By understanding the relative direction and magnitude of two vectors, it is possible to determine the vector with the largest (positive) x component when added together.
Vector addition is essentially the act of combining two or more vectors to determine the magnitude and direction of the resulting vector. When two vectors are added, each vector is represented with two components- a magnitude and a direction. When the two vectors are added together, their respective magnitudes and direction will be combined to give you the resulting vector. The result may be greater, equal, or less than either of the two vectors.
For example, if you have two vectors, A and B, and you want to determine which two vectors, when added, will have the largest (positive) x component, you must first consider the magnitude and directions of the two input vectors. If A has a longer magnitude than B, and it’s direction is pointing towards an x-coordinate of say, +3, then the resulting vector will have a larger (positive) x component if A is added to B rather than if B is added to A. Furthermore, even if A and B have similar magnitudes, the vector with the higher x-coordinate will give a larger (positive) x component when added to the other.
Another factor that may contribute to the resulting vector having a larger (positive) x component is if the two vectors when added together form an acute or obtuse angle. If each vector is pointing in the same direction and forming an acute angle, then the resulting vector will have a larger (positive) x component than if the angle formed was obtuse. This is because in an acute angle, both vectors are in the same direction and when combined, the resulting vector’s magnitude and direction are going in the same direction as the original vectors, making for the largest (positive) x component when added.
Finally, one should also consider the angle formed between the two vectors in relation to the x-axis. If the angle formed between the two vectors and the x-axis is in the same direction as the x-axis, the vector combination will have the largest (positive) x component. On the other hand, if the angle formed between the two vectors and the x-axis is opposite to the direction of the x-axis, the resulting vector will not have the largest (positive) x component.
In conclusion, when considering which two vectors, when added, will have the largest (positive) x component, one should consider the magnitude of each vector, the angle formed between the two vectors and the x-axis and the angle formed between the two vectors when added together. The vector which has the longest magnitude and the most acute angle in relation to the x-axis and the resulting vector when added together will have the largest (positive) x component when added.