To find the component form of the vector obtained by adding vector u and vector v, we first need to understand what these vectors represent.
Given:
- Vector u = (5, 3)
- Vector v = (1, 4)
The component form of a vector is typically represented as (x, y), where x and y are the sums of the corresponding components of the two vectors. In this case, you can find the component form of vector u + v by adding the corresponding components:
- Add the x-components: 5 + 1 = 6
- Add the y-components: 3 + 4 = 7
Therefore, the component form of the vector u + v is:
(6, 7)
This means that the resulting vector has a x-component of 6 and a y-component of 7. We can visualize this graphically; if you start at the origin (0, 0), the endpoint of the resultant vector (6, 7) will be located at the point (6, 7) on a Cartesian plane.