Subtracting vectors graphically is achieved by adding the negative of the vector being subtracted to the first vector. This method leverages the principles of vector addition.
Understanding Vector Subtraction
In vector algebra, subtracting one vector from another, say vector B from vector A (A - B), is equivalent to adding vector A to the negative of vector B (A + (-B)).
This key principle from the reference is fundamental: In subtracting vectors recall that it is done by adding a negative vector.
What is a Negative Vector?
A negative vector, denoted as -B, is a vector that has the same magnitude as the original vector B but points in the exact opposite direction.
Steps for Graphical Vector Subtraction (A - B)
To graphically subtract vector B from vector A (A - B), follow these steps:
- Identify the Vectors: Start with the two vectors, A and B, you want to subtract.
- Find the Negative Vector (-B): Draw vector B but reverse its direction. Ensure the length (magnitude) remains the same. This new vector is -B.
- Position the Vectors for Addition: Place the tail of the negative vector (-B) at the head (tip) of the first vector (A). This is the standard head-to-tail method for vector addition.
- Draw the Resultant Vector: Draw a new vector starting from the tail of the first vector (A) and ending at the head of the negative vector (-B).
- Label the Resultant: This new vector represents the resultant vector of the subtraction, A - B.
This graphical representation of A + (-B) shows the resultant vector connecting the starting point (tail of A) to the ending point (head of -B), effectively illustrating the subtraction.
Graphical Subtraction Summary
| Step | Action | Outcome |
|---|---|---|
| 1. Start with Vectors | Have vectors A and B. | Original problem A - B. |
| 2. Find Negative Vector | Draw -B (same magnitude, opposite dir). | Represents -B. |
| 3. Position for Addition | Place tail of -B at head of A. | Set up for A + (-B). |
| 4. Draw Resultant | Connect tail of A to head of -B. | The resultant vector is drawn. |
| 5. Label Resultant | Label the new vector as A - B. | Final answer to graphical subtraction. |
Using this method, you can visually determine both the magnitude (length) and direction of the resulting vector from the subtraction.
