Subtraction of 2 Vectors

Subtracting vectors involves adding the additive inverse of the second vector to the first. This means reversing the direction of the second vector and then performing vector addition.

Vectors have two main components:

Magnitude: This is the length of the vector.

Direction: This indicates the orientation of the vector in space.

When subtracting vectors, students should follow these steps:

Reverse direction: Change the direction of the second vector to find its additive inverse.

Add vectors: Perform vector addition by adding the corresponding components of the vectors.

Resultant vector: The resultant vector represents the difference between the two original vectors.

The following are methods for subtracting vectors:

Method 1: Component Method

To apply the component method for vector subtraction, use the following steps.

Step 1: Break both vectors into their components.

Step 2: Reverse the direction of the second vector by changing the signs of its components.

Step 3: Add the components. Example: Subtract vector B from vector A.

Step 1: Write components of vectors A and B.

Step 2: Reverse the components of vector B.

Step 3: Add the components together. Answer:

Method 2: Graphical Method

When subtracting vectors graphically, draw the vectors with their tails at the same point. Reverse the direction of the second vector and then complete the parallelogram. The resultant vector is the diagonal.

For example, subtract vector B from vector A.

Solution: Draw vector A. Draw vector B with reversed direction. Complete the parallelogram to find the resultant vector.

In vector operations, subtraction has some characteristic properties:

• Subtraction is not commutative In vector subtraction, reversing the order changes the result, i.e., A - B ≠ B - A.

• Subtraction is not associative Involving three or more vectors, changing the grouping changes the result. (A − B) − C ≠ A − (B − C)

• Subtraction as addition of the opposite Subtracting a vector is the same as adding its opposite, so vector subtraction can be viewed as vector addition with the direction reversed. A − B = A + (−B)

• Subtracting zero vector leaves the vector unchanged Subtracting the zero vector from any vector results in the same vector: A - 0 = A.

Tips and tricks are useful for students to efficiently deal with vector subtraction. Some helpful tips are listed below:

Tip 1: Pay attention to both magnitude and direction when reversing a vector.

Tip 2: Use graph paper or vector tools to accurately draw vectors and find the resultant.

Tip 3: Break vectors into components to simplify calculations, especially in 2D or 3D space.

Subtraction in vector mathematics can be challenging, often leading to common mistakes. However, being aware of these errors can help students avoid them.