The triangle law of vector addition states that if two vectors are represented by two sides of a triangle taken in order, then their resultant is represented by the third side of the triangle taken in the opposite direction.
Formula:
The formula for the triangle law of vector addition is:
R = A + B
where:
- R is the resultant vector
- A and B are the two vectors being added
Graphical Representation:
The triangle law can be visually represented as follows:
- Draw the first vector A with its tail at the origin.
- Draw the second vector B with its tail at the head of vector A.
- Draw the resultant vector R from the tail of A to the head of B.
This forms a triangle where the sides represent the vectors A, B, and R.
Practical Applications:
The triangle law of vector addition has numerous applications in various fields, including:
- Physics: Calculating forces, velocities, and displacements
- Engineering: Analyzing structural loads and forces
- Navigation: Determining the course and distance traveled
Example:
Let's say you have two vectors:
- A = (3, 4)
- B = (1, 2)
To find the resultant vector R, you can use the triangle law:
R = A + B = (3 + 1, 4 + 2) = (4, 6)
Therefore, the resultant vector R is (4, 6).
