Addition And Subtraction of Vectors - SS1 Physics Lesson Note

Addition and subtraction of vectors involve combining two or more vectors to determine their resultant or net vector. The process of vector addition and subtraction takes into account both the magnitude and direction of the vectors. Let's explore how to perform these operations:

1. Addition of Vectors:

   To add vectors, you can use either graphical or component methods.

   Graphical Method:

• Draw the vectors to scale on a coordinate system, making sure to maintain their given directions.

Place the tail of the second vector at the head of the first vector.

The resultant vector is the vector that connects the tail of the first vector to the head of the second vector.

Measure the magnitude and direction of the resultant vector.

 

 

Component Method:

• Resolve the vectors into their horizontal (x-axis) and vertical (y-axis) components.

Add the respective components together.

The resultant vector's magnitude can be found using the Pythagorean theorem: 

magnitude = √(Rx^2 + Ry^2)

• The direction of the resultant vector can be found using trigonometry: direction = tan^(-1)(Ry/Rx).

2. Subtraction of Vectors:

   To subtract vectors, you can use the same graphical or component methods as for addition.

   Graphical Method:

   - Draw the first vector to scale on a coordinate system.

   - Draw the second vector in the opposite direction from the tail of the first vector.

   - The resultant vector is the vector that connects the tail of the first vector to the head of the second vector.

   - Measure the magnitude and direction of the resultant vector.

   Component Method:

   - Resolve the vectors into their horizontal (x-axis) and vertical (y-axis) components.

   - Subtract the respective components of the second vector from the first vector.

   - The resultant vector's magnitude and direction can be calculated using the same methods as in vector addition.

It's important to note that vectors must be in the same coordinate system and units to perform vector addition or subtraction. Additionally, vector addition and subtraction follow the rules of vector algebra, including the commutative and associative properties.

By performing vector addition and subtraction, you can determine the resultant vector, which represents the combined effect or displacement resulting from the individual vectors.