Understanding component-wise operations
Several vector operations are just component-wise operations. A component-wise operation is one that you perform on each component of a vector or on like components of two vectors. Like components are components that have the same subscript. The component-wise operations that you will implement are as follows:
- Vector addition
- Vector subtraction
- Vector scaling
- Multiplying vectors
- Dot product
Let's look at each of these in more detail.
Adding two vectors together yields a third vector, which has the combined displacement of both input vectors. Vector addition is a component-wise operation; to perform it, you need to add like components.
To visualize the addition of two vectors, draw the base of the second vector at the tip of the first vector. Next, draw an arrow from the base of the first vector to the tip of the second vector. This arrow represents the vector that is the result of the...