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

Verified step by step guidance

1. Identify the components of the vector given in angle bracket notation. Here, the vector is \( \langle 2, 0 \rangle \), where 2 is the x-component and 0 is the y-component.
2. Recall that the vector in the form \( a \mathbf{i} + b \mathbf{j} \) means \( a \) is the coefficient of the unit vector \( \mathbf{i} \) along the x-axis, and \( b \) is the coefficient of the unit vector \( \mathbf{j} \) along the y-axis.
3. Assign the x-component of the vector to \( a \) and the y-component to \( b \). So, \( a = 2 \) and \( b = 0 \).
4. Write the vector in the form \( a \mathbf{i} + b \mathbf{j} \) by substituting the values: \( 2 \mathbf{i} + 0 \mathbf{j} \).
5. Simplify the expression by removing the zero term if desired, resulting in \( 2 \mathbf{i} \).

Key Concepts

Vector Representation in Component Form

Vectors in two dimensions can be expressed as a combination of unit vectors i and j, where i represents the x-axis direction and j represents the y-axis direction. Writing a vector as a i + b j means expressing it in terms of its horizontal (a) and vertical (b) components.

Unit Vectors i and j

The unit vectors i and j are standard basis vectors in 2D space, with i = 〈1, 0〉 pointing along the x-axis and j = 〈0, 1〉 pointing along the y-axis. They serve as building blocks to represent any vector by scaling and adding these units.

Converting Coordinate Notation to Vector Form

A vector given in coordinate form 〈x, y〉 can be rewritten as x i + y j by associating the first component with i and the second with j. This conversion helps in vector operations and visualizing vectors in terms of directions.