Write each vector in the form a i + b j.
〈2, 0〉

Verified step by step guidance

1. Identify the components of the vector 〈2, 0〉. Here, the first component is 2 and the second component is 0.
2. Understand that the vector 〈2, 0〉 can be expressed in terms of the unit vectors **i** and **j**.
3. The unit vector **i** represents the x-direction, and the unit vector **j** represents the y-direction.
4. Multiply the first component (2) by the unit vector **i** to get the x-component of the vector: 2i.
5. Multiply the second component (0) by the unit vector **j** to get the y-component of the vector: 0j.

Key Concepts

Vector Representation

Vectors can be represented in a Cartesian coordinate system using unit vectors. The standard form of a vector in two dimensions is expressed as 'a i + b j', where 'a' is the component along the x-axis (i) and 'b' is the component along the y-axis (j). This notation allows for easy manipulation and understanding of vector quantities.

Components of a Vector

The components of a vector indicate its magnitude in each direction of the coordinate system. For the vector 〈2, 0〉, the first component '2' represents the horizontal (x-axis) movement, while the second component '0' indicates no movement in the vertical (y-axis) direction. Understanding these components is crucial for converting vectors into their standard form.

Unit Vectors

Unit vectors are vectors with a magnitude of one, used to indicate direction. In the context of vector representation, 'i' and 'j' are unit vectors that point in the positive x and y directions, respectively. They serve as the building blocks for expressing any vector in the plane, allowing for clear communication of direction and magnitude.