How Do You Find the Vector of Two Vectors?

This question is a bit ambiguous. It could be asking about several different vector operations:

1. Finding the Vector Sum

To find the vector sum of two vectors, you simply add their corresponding components.

• Example:
  • Vector A = (2, 3)
  • Vector B = (1, -1)
  • Vector A + Vector B = (2 + 1, 3 + (-1)) = (3, 2)

2. Finding the Vector Difference

To find the vector difference of two vectors, you subtract their corresponding components.

• Example:
  • Vector A = (2, 3)
  • Vector B = (1, -1)
  • Vector A - Vector B = (2 - 1, 3 - (-1)) = (1, 4)

3. Finding the Vector Product

There are two types of vector products:

• Dot Product: The dot product of two vectors results in a scalar value. It is calculated by multiplying corresponding components and summing the results.
  • Example:
    • Vector A = (2, 3)
    • Vector B = (1, -1)
    • Vector A · Vector B = (2 1) + (3 -1) = -1
• Cross Product: The cross product of two vectors results in a new vector that is perpendicular to both original vectors. It is calculated using a specific formula.
  • Example:
    • Vector A = (2, 3, 0)
    • Vector B = (1, -1, 0)
    • Vector A x Vector B = (0, 0, -5)

4. Finding the Vector Projection

The vector projection of one vector onto another is the component of the first vector that lies in the direction of the second vector. It is calculated using a specific formula.

• Example:
  • Vector A = (2, 3)
  • Vector B = (1, -1)
  • Projection of A onto B = ((A · B) / (B · B)) B = (-1 / 2) (1, -1) = (-1/2, 1/2)

By understanding these different vector operations, you can find the relevant "vector of two vectors" depending on the specific context of your problem.