Subtraction of Vectors
Big Idea:
Just as we can subtract numbers, we can subtract vectors. Vector subtraction is a fundamental operation in geometry and physics that helps us find the difference between two directed quantities — like finding the displacement from one point to another.
📐 What is a Vector?
A vector is a quantity that has both magnitude (size) and direction. We represent vectors as arrows or as ordered pairs of components.
If $\vec{a} = (a_x, a_y)$, then:
- $a_x$ is the horizontal component (x-direction)
- $a_y$ is the vertical component (y-direction)
The magnitude is: $|\vec{a}| = \sqrt{a_x^2 + a_y^2}$
➖ The Negative of a Vector
Before we subtract, we need to understand the negative (or opposite) of a vector:
If $\vec{a} = (a_x, a_y)$, then:
$$-\vec{a} = (-a_x, -a_y)$$
The negative of a vector has the same magnitude but opposite direction. It's like flipping the arrow around!