Write each vector in the form a i + b j.
〈6, -3〉

Key Concepts

Vectors

A vector is a mathematical object that has both magnitude and direction. In a two-dimensional space, vectors can be represented in the form 'a i + b j', where 'a' and 'b' are the components along the x-axis and y-axis, respectively. This representation allows for easy manipulation and understanding of the vector's properties.

Component Form

The component form of a vector expresses it in terms of its horizontal and vertical components. For example, the vector 〈6, -3〉 can be written as 6 i - 3 j, indicating it moves 6 units in the positive x-direction and 3 units in the negative y-direction. This form is essential for performing vector operations such as addition and scalar multiplication.

Unit Vectors

Unit vectors are vectors with a magnitude of one, used to indicate direction. The standard unit vectors in two dimensions are 'i' (1, 0) and 'j' (0, 1). By expressing vectors in terms of unit vectors, we can simplify calculations and better understand the direction and orientation of the vector in the coordinate system.