Maybe, you all already know that a unit vector is a special quantity that has a magnitude of one. However, you also need to keep in mind that the non-zero vectors will always have a corresponding unit vector which will have the same direction as that particular vector, but the magnitude will be of one. Look at this website, by dividing the vector by its magnitude you can find out the unit vector. On the other hand, there are some simple ideas that you can choose for finding the unit vector of the given vector.
Basic things you should know about unit vectors
In mathematics, there is a special kind of vector which is known as a unit vector. The same unit vector can be beneficial in Physics as well. If you want to define a unit vector then you can say that the unit vector will always have a magnitude one and you will not have any units.
• Unit vector will be denoted by a letter mark with a circumflex
• If B is a distance then the unit vector of B will be B-hat.
• When you multiply a unit vector bi a scalar or which is having magnitude 1 and no units, the resulting a vector may have a magnitude equal to the value with the units of this scalar.
These are some of the basic things that one should always know about the unit vector. Once you become familiar with the basics of unit vectors, it might be easy for you to understand the entire procedure of calculating the unit vectors.
Find the unit vector of a vector
In many situations, the vector components can be given. Consequently, you can convert the given vector components to the magnitude for angle by using some trigonometry methods. First of all, let a vector PQ is having a magnitude of 1. Then you will divide the vector PQ by its magnitude in order to find the unit vector. The magnitude will be written in the form ||PQ||. How do you find the unit vector? This is the fundamental things you need to know about the unit vectors.
How to find a unit vector in the same direction
Now, you have successfully become familiar with lots of things regarding the unit vector. Consequently, it becomes important for you to understand how you can find out a unit vector in the same direction.
Let you have r = xi + yj + zk
From this expression, it is completely clear that the unit vector is in the same direction as the vector R is simply the vector is divided by its magnitude. In general, it can be expressed as: r-hat= vector r/||r||.
Calculate the magnitude of the vector
After becoming familiar with the basics now, you will have to find out the magnitude of the vector for finding a unit vector in the same direction. You need to keep in mind that the magnitude of a vector can be expressed by the square root of the sum of the squares of its components. How do you find the unit vector? Let’s check the final step:
If X, Y, and Z are the components then the magnitude of the vector r will be
r= √x2+y2+z2
Then use it in the expression r-hat= vector r/|| r|| which can be prolonged as: r= xi + yj + zk/r. The result makes it clear that each component of the unit vector is simply the corresponding component, of the original vector, divided by the magnitude r=√x2+y2+z2 of the original vector. Now, you have successfully collected information about calculating the unit vector of the given vector in the same direction.