How do you add vectors (1, 1) and (-1, -1)?

To add vectors (1, 1) and (-1, -1), you combine their corresponding components to get (0, 0).

When adding vectors, you simply add their corresponding components. Vectors are often written in the form (x, y), where x is the horizontal component and y is the vertical component. For the vectors (1, 1) and (-1, -1), you add the x-components together and the y-components together.

First, let's add the x-components: 1 + (-1). This equals 0. Next, add the y-components: 1 + (-1). This also equals 0. So, when you combine the vectors (1, 1) and (-1, -1), the result is the vector (0, 0).

This process can be visualised on a graph. If you start at the origin (0, 0) and move 1 unit to the right and 1 unit up (following the vector (1, 1)), you reach the point (1, 1). Then, if you move 1 unit to the left and 1 unit down (following the vector (-1, -1)), you return to the origin (0, 0). This shows that the vectors (1, 1) and (-1, -1) cancel each other out, resulting in the zero vector (0, 0).

Understanding vector addition is crucial in many areas of mathematics and physics, as it helps describe movements and forces in a plane. By mastering this basic concept, you'll be better equipped to tackle more complex problems involving vectors.