To draw the resultant vector of two vectors being added, follow the "head-to-tail" method:
-
Draw the First Vector: Draw the first vector to scale, representing its magnitude and direction. This is your starting point.
-
Draw the Second Vector: Starting at the head (arrow tip) of the first vector, draw the second vector to the same scale, accurately representing its magnitude and direction. This essentially places the tail of the second vector at the head of the first.
-
Draw the Resultant Vector: Draw a vector from the tail (starting point) of the first vector to the head (arrow tip) of the second vector. This new vector represents the resultant vector (R).
-
Label: Label the first vector (e.g., V1), the second vector (e.g., V2), and the resultant vector (R). Indicate the magnitude and direction of each vector on the diagram, especially the resultant vector. The magnitude can be determined by measuring the length of the resultant vector to the same scale used for V1 and V2. The direction can be specified by its angle relative to a reference direction (e.g., the x-axis).
Example:
Imagine adding vector A (5 units to the right) and vector B (3 units upwards).
- Draw vector A, 5 units long, pointing to the right.
- Starting at the tip of vector A, draw vector B, 3 units long, pointing upwards.
- Draw a line from the tail of vector A to the tip of vector B. This is the resultant vector R.
- The magnitude of R is approximately 5.83 units (calculated using the Pythagorean theorem: sqrt(5^2 + 3^2)). The direction can be specified as approximately 31 degrees above the horizontal (calculated using arctan(3/5)).
Important Considerations:
- Scale: Using a consistent scale is crucial for accurately representing magnitudes.
- Direction: Correctly representing the direction of each vector is essential for obtaining the correct resultant vector.
- Parallelogram Method: An alternative method is the parallelogram method. Draw both vectors from a common origin. Complete the parallelogram, and the diagonal from the origin to the opposite vertex is the resultant. This is mathematically equivalent to the head-to-tail method.
