How to find the coordinates of the vector

Finding the coordinates of the vector quite frequently found the condition of many tasks in mathematics. The ability to find the coordinates of the vector will help you in other, more complex tasks with similar subjects. In this article, we will look at the formula of finding the coordinates of the vector and several tasks.

1

Finding the coordinates of the vector in the plane

What is a plane? The plane is considered a two-dimensional space, a space with two dimensions (Measure X and the measurement Y). For example, paper is a plane. Table surface - plane. Any optional figure (square, triangle, trapezium) is also a plane. Thus, if the task condition needs to find the coordinates of the vector, which lies on the plane, immediately remember about X and Y. Find the coordinates of this vector as follows: The coordinates of the vector \u003d (XB - Xa; YB - XA). From the formula, it can be seen that the coordinates of the endpoint need to take the coordinates of the starting point.

Example:

• The vector CD has an initial (5; 6) and finite (7; 8) coordinates.
• Find the coordinates of the vector itself.
• Using the above-mentioned formula, we obtain the following expression: CD \u003d (7-5; 8-6) \u003d (2; 2).
• Thus, the coordinates of the CD vector \u003d (2; 2).
• Accordingly, X coordinate is equal to two, y coordinate - also two.

2

Finding the coordinates of the vector in space

What is space? Space is already dimensional measurement, wherein given three coordinates: x, y, z. In case you need to find a vector that lies in space, the formula is practically not changed. Only one coordinate is added. To find a vector, you need to take the start coordinates from the end coordinates. AB \u003d (XB - Xa; YB - Ya; ZB - ZA)

Example:

• The DF vector has an initial (2; 3; 1) and finite (1; 5; 2).
• Applying the above formula, we obtain the vector coordinates DF \u003d (1-2; 5-3; 2-1) \u003d (-1; 2; 1).
• Remember, the coordinate value may be negative, there is no problem.

3

How to find the coordinates of online?

If for some reason you do not want to find the coordinates yourself, you can use online calculator. To begin with, select the dimension of the vector. The dimension of the vector is responsible for its measurement. Dimension 3 means that the vector is in space, dimension 2 - that on the plane. Next, insert the coordinates of the points to the appropriate fields and the program will determine you the coordinates of the vector itself. Everything is very simple.

By clicking on the button, the page will automatically scroll down and gives you the correct answer together with the solutions stages.

It is recommended to explore this topic well, because the concept of the vector is found not only in mathematics, but also in physics. Students of the Faculty of Information Technologies also explore the theme of vectors, but at a more complex level.