How do you write vector b in terms of i and j?

Vector **b** can be written as **b = bi + cj**, where **b** and **c** are its components.

In more detail, vectors are mathematical objects that have both a magnitude (length) and a direction. When we talk about vectors in a 2-dimensional space, we often use the unit vectors **i** and **j** to represent the directions along the x-axis and y-axis, respectively. The unit vector **i** points in the direction of the positive x-axis, and the unit vector **j** points in the direction of the positive y-axis.

To express a vector **b** in terms of **i** and **j**, we need to know its components along the x and y axes. Let's say the vector **b** has an x-component of **b** and a y-component of **c**. This means that the vector **b** moves **b** units in the direction of the x-axis and **c** units in the direction of the y-axis.

We can then write the vector **b** as a combination of these movements: **b = bi + cj**. Here, **bi** represents the movement along the x-axis, and **cj** represents the movement along the y-axis. By adding these two components together, we get the full vector **b**.

This way of writing vectors helps us to easily visualise and work with them, especially when performing operations like addition, subtraction, and scalar multiplication. It also makes it simpler to analyse the vector's direction and magnitude.