Among the top quantities you use in mathematics, engineering, and physics, the vector is a special quantity which has magnitude and direction. According to Calculator Academy, the vector can be defined as an arithmetical object which always has direction and magnitude. For determining the position of one point in space relative to another, the vector can be used in physics and mathematics. Somehow, people can find it difficult to calculate the vector of any given question. This is why you need to go through the following paragraphs where you can collect comprehensive information regarding the formula for a vector.
On the other hand, it is important for you to collect some important information about the unit vector. This is yet another special vector quantity which is having a magnitude of one. There could be various rules for finding out the unit vector with the same direction of a given vector. The magnitude will always be a value when you are talking about a unit vector. Overall, you need to be familiar with a special formula that can help you to calculate the unit vector quickly.
The formula for a unit vector
At the present moment, you have successfully collected basic details about a vector and unit vector. To know what is the formula for a unit vector, it’s really important to know something called basics about the unit vectors. Let’s check out some popular formula that you can use for unit vector.
Divide the unit vector by its magnitude
In a situation when you have to find out the unit vector in the same direction of the vector, you can go with this simple formula. Let v be a unit vector which is having direction and magnitude of 1, a* will be the vector with direction and magnitude. Likewise, you can assume b* as the magnitude of the vector. Then you can write down the formula as:
Unit Vector= vector/ magnitude of vector, or v= a/b
Where v denotes to the vector unit, a* denoted the vector with direction and magnitude and b* denotes the magnitude of the vector. By making use of this is a simple formula, it might be easy for people to calculate the unit vector.
Axes of unit vectors
X is an expression used for showing the value of the vector in the x-axis. On the other hand, to show the value of the vector in the y-axis, y will be used. Likewise, z denotes the value of the vector in the Z-axis.
Components of a unit vector
What is the formula for a unit vector? When you are searching around for possible solutions of the same question, you need to have comprehensive information about the components of a unit vector. Whenever a unit vector will be expressed in the Cartesian format, i, j, k are its three scalar mechanisms which can be called as direction cosines.
The value of every element is equivalent to the cosine of the slant shaped by the unit vector with the relevant foundation vector. Now, you may have successfully understood the formula for unit vector with the help of available information.