-(1-2)-and-(0-3)-(%E2%80%931-0)-and-(2-0)-(2-1).jpeg "(1 2) (1 2) And (0 3) (–1 0) And (2 0) (2 1)")
Operating with Vectors
In this article, we will explore how to operate with vectors using examples (1, 2) and (1, 2), (0, 3) and (-1, 0), and (2, 0) and (2, 1).
Addition of Vectors
The addition of vectors is performed by adding corresponding components. Let's consider the vectors (1, 2) and (1, 2).
(1, 2) + (1, 2) = ?
To add these vectors, we add the x-components and the y-components separately:
x-component: 1 + 1 = 2 y-component: 2 + 2 = 4
So, the result is (2, 4).
Subtraction of Vectors
The subtraction of vectors is performed by subtracting corresponding components. Let's consider the vectors (0, 3) and (-1, 0).
(0, 3) - (-1, 0) = ?
To subtract these vectors, we subtract the x-components and the y-components separately:
x-component: 0 - (-1) = 1 y-component: 3 - 0 = 3
So, the result is (1, 3).
Scalar Multiplication
Scalar multiplication is performed by multiplying each component of the vector by a scalar value. Let's consider the vectors (2, 0) and (2, 1).
2 * (2, 0) = ?
To multiply the vector by 2, we multiply each component by 2:
x-component: 2 * 2 = 4 y-component: 2 * 0 = 0
So, the result is (4, 0).
Vector Equality
Two vectors are equal if and only if their corresponding components are equal. Let's consider the vectors (2, 0) and (2, 1).
(2, 0) = (2, 1) ?
In this case, the x-components are equal (2 = 2), but the y-components are not equal (0 ≠ 1). Therefore, the vectors are not equal.
In conclusion, operating with vectors involves adding, subtracting, and scaling vectors. By following the rules of vector operations, we can perform various mathematical operations on vectors.
