The Formula for Vector Subtraction

Oct 13, 2025 by thesweetdesigns.com 97 views

Introduction

Vectors are mathematical objects that have both magnitude and direction. They are used to represent quantities with both size and direction, such as forces, velocities, and displacements. In this article, we will explore the concept of vector subtraction, which is a fundamental operation in vector algebra.

What is Vector Subtraction?

Vector subtraction is the process of finding the difference between two vectors. It is denoted by the symbol - and is used to find the vector that points from the tip of one vector to the tip of another vector. In other words, it is the vector that results from subtracting the components of one vector from the components of another vector.

The Formula for Vector Subtraction

The formula for vector subtraction is given by:

\vec{a} - \vec{b} = \{a_1 - b_1, a_2 - b_2\}

where $\vec{a} = \{a_1, a_2\}$ and $\vec{b} = \{b_1, b_2\}$ are two vectors in a two-dimensional space.

Example: Finding $\vec{a} - \vec{b}$

Let's consider the example given in the problem statement:

\vec{a} = \{2, 3\}

\vec{b} = \{1, 5\}

To find $\vec{a} - \vec{b}$ , we simply subtract the components of $\vec{b}$ from the components of $\vec{a}$ :

\vec{a} - \vec{b} = \{2 - 1, 3 - 5\}

\vec{a} - \vec{b} = \{1, -2\}

Conclusion

In this article, we have explored the concept of vector subtraction and provided a step-by-step guide on how to find the difference between two vectors. We have also used the example given in the problem statement to illustrate the concept. Vector subtraction is a fundamental operation in vector algebra and is used extensively in physics, engineering, and other fields.

Answer

The correct answer is:

D. $\{1,-2\}$

Discussion

Q&A: Frequently Asked Questions

Q: What is vector subtraction?

A: Vector subtraction is the process of finding the difference between two vectors. It is denoted by the symbol - and is used to find the vector that points from the tip of one vector to the tip of another vector.

Q: What is the formula for vector subtraction?

A: The formula for vector subtraction is given by:

\vec{a} - \vec{b} = \{a_1 - b_1, a_2 - b_2\}

where $\vec{a} = \{a_1, a_2\}$ and $\vec{b} = \{b_1, b_2\}$ are two vectors in a two-dimensional space.

Q: How do I find the difference between two vectors?

A: To find the difference between two vectors, you simply subtract the components of one vector from the components of another vector. For example, if $\vec{a} = \{2, 3\}$ and $\vec{b} = \{1, 5\}$ , then $\vec{a} - \vec{b} = \{2 - 1, 3 - 5\} = \{1, -2\}$ .

Q: What is the result of vector subtraction?

A: The result of vector subtraction is a new vector that points from the tip of one vector to the tip of another vector. The magnitude and direction of the resulting vector depend on the magnitudes and directions of the original vectors.

Q: Can I subtract a vector from itself?

A: Yes, you can subtract a vector from itself. In this case, the result will be a zero vector, which has no magnitude and no direction.

Q: Can I subtract a vector from a scalar?

A: No, you cannot subtract a vector from a scalar. Vector subtraction is only defined for vectors, not for scalars.

Q: Can I subtract two vectors in three-dimensional space?

A: Yes, you can subtract two vectors in three-dimensional space. The formula for vector subtraction is the same as in two-dimensional space, but you need to consider the third component of the vectors.

Q: What are some common applications of vector subtraction?

A: Vector subtraction has many applications in physics, engineering, and other fields. Some common applications include:

Finding the difference between two forces or velocities
Calculating the displacement between two points
Determining the position of an object in a coordinate system
Analyzing the motion of an object in a two- or three-dimensional space

Conclusion

In this article, we have provided a comprehensive guide to vector subtraction, including the formula, examples, and frequently asked questions. We hope that this article has been helpful in understanding the concept of vector subtraction and its applications in various fields.