How do You Calculate a Vector?

Indeed, the vector is a quantity that contains two pieces of information one which is the direction and another one is the magnitude/length. You can visualize the vector on a graph where X, Y and Z axis have been plotted. As mentioned, the vector is a quantity that contains direction and magnitude, if you calculate the value of both direction and magnitude you can easily calculate a vector. Whenever you will have to solve some questions on the vector, you should directly find out the magnitude and the direction of the vector. To know more about calculating a vector, you can explore the following paragraphs without asking.

Introduction to the vectors

In the beginning, you need to keep in mind that the vector functions always operate on three-dimensional vectors. In addition, the vectors can be used for various purposes. You can use the vectors for describing X, Y, and Z position. Likewise, you can describe the direction of speed with the help of the vector.

You all know that a vector is a special quantity having magnitude and direction. A vector can consist of several numbers. On a graph, you can imagine a vector as an arrow. However, some professionals can visualize a vector as a collection of numbers. How do you calculate a vector? This can be an important question for you and that’s why you have to be familiar with the introduction part.

Proper ways to calculate the vectors

Now, you have successfully collected some basic details about the vector, and that’s why you need to be familiar with some proper ways to calculate the vector.

General formula:

First of all, you can think about the most common formula that can be used for calculating the vector. Make sure that you will not commit a single mistake while taking action on this formula to find out the vector easily. Let’s take a brief look at the general formula of finding a vector in which you have to find magnitude and direction of the vector:

Find out the magnitude of the vector

The magnitude of a vector is the distance between the initial point and the endpoint. In symbols, the magnitude of the vector is written as |….|.

Find out the direction of the vector

One should always keep in mind that the direction of a vector is measured as the angle that the vector makes with any horizontal line. There are a number of formulas that you can use in order to calculate the direction of the given vector in a short amount of time.

The formula tanθ=Y/X is a very popular formula to calculate the direction of a vector. In this formula, X is the horizontal change and Y denotes the vertical change. In order to check how do you calculate a vector this is a crucial thing.

Tanθ=y2 − y1/x2 − x1

If the previously mentioned formula doesn’t work for you to calculate the direction of a vector, you can go with this one. In this formula, X1 Y1 are the initial points and X2, Y2 are the terminal points.

Distance Formula for the magnitude

If the coordinates of the original point and the endpoint of a vector are prearranged, then the distance method can be used to discover its magnitude. Now, you may not face further problem to calculate the vectors.

In some situation, if the coordinates of endpoint as well as the initial point of a vector are given, it might be the best time for you to use the distance formula and find out the magnitude of the vector. Now you just need to take your time and have the rest of the benefits with the formula of calculating vector.