What is the representation of vector s in the form ai + bj?

The representation of vector s in the form ai + bj is s = ai + bj, where a and b are its components.

In more detail, vectors are mathematical objects that have both magnitude and direction. When we represent a vector in the form ai + bj, we are expressing it in terms of its horizontal (i) and vertical (j) components. Here, 'a' is the coefficient of the unit vector i, which points in the horizontal direction (along the x-axis), and 'b' is the coefficient of the unit vector j, which points in the vertical direction (along the y-axis).

For example, if vector s has components 3 and 4, it can be written as s = 3i + 4j. This means that the vector moves 3 units in the horizontal direction and 4 units in the vertical direction. The unit vectors i and j are standard notations used to indicate directions along the x-axis and y-axis, respectively.

To find the components 'a' and 'b' of a vector, you can use its coordinates. If a vector starts at the origin (0,0) and ends at the point (x,y), then 'a' is equal to x and 'b' is equal to y. For instance, if a vector ends at the point (5, -2), it can be written as s = 5i - 2j.

Understanding this representation helps in performing various vector operations such as addition, subtraction, and finding the magnitude or direction of the vector.