Published on March 31st, 2012 | by BeScientist.info2
Cross product and Dot product of Vectors
Guys you all know, these are easy concepts of math but sometimes it’s really hard to differentiate which one is cross product and which one is dot product if you don’t work with these for a long time. In this tutorial I will help you guys with several questions of these cross and dot products. I will also make you understand the physical significance of these products. Let’s begin now,
I guess you guys know what does vector means. The characteristics of vector are
1) They have magnitude and
2) They have direction
Scalar quantities don’t have second property i.e. direction.
But what does something have direction means. Most of you think, it’s easy and it is easy but some of you might have problem figuring it out. To grasp this concept see the picture below( picture of vector)
So, what would scalar look like?
It’s easy to know this concept but it’s sometimes hard to differentiate between scalar and vector quantities. For an instance, let’s take an example of Temperature. We can presume temperature is a vector in a sense that temperature always flows from high temperature to low temperature but in fact, we don’t need any direction to describe it. Meaning, let’s say you say your body temperature is 94 degree Fahrenheit . You don’t ask which direction is 94 degree Fahrenheit is.
But, lets say Velocity( not speed), the definition velocity is such that it needs direction to describe it. For example, if someone said a car is moving at velocity 30 m/s, it’s incomplete. Because you necessarily need direction to describe velocity. You need to say 30 m/s in north or south or west or east or any other direction. That’s mandatory.
Looks easy but you need to use your brain for some quantities to identify it is vector or scalar. Most of them makes sense once you hear the word but the genuine way is to listen to the definition of the quantity.
Below are list of some of scalar and vector quantities obtained from NASA website:
So, Now you grasped the concept of vector and scalar quantities. Now, let’s get into vector products:
The two types of products are
1) Cross Product and
2) Dot Product
Now, when you multiply two vectors, then you will get another vector that will be perpendicular to BOTH of the multiplied vectors. This is why you will get third vector in another dimension.
Her is a nice Simulation:
The mathematical formula is
A × B =|A||B| sin(θ)
here |A| and |B| are the magnitudes of A and B respectively.
Physical meaning of cross product of vector represents the area of the parallelogram bounded by sides of length A and B and having angle θ between A and B.
Now for dot product;
When two vectors are multiplied, we don’t only get vectors, we also get scalar, that is called dot product.
These are the differences between cross product and dot product of vectors.
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