Difference Between Dot Product vs Cross Product
To understand the difference between dot product and cross product, you must grasp the definitions first. As you already know, these are common terms used in certain subjects such as mathematics and physics. With good knowledge of the concept, one can calculate and analyze certain entities.
Keep in mind that a vector quantity is an object that has a size and direction while a scalar quantity has size without direction. The methods of manipulating vectors form the subject of this guide. That said, we will kick off with their definitions and later draw the distinction.
Definition of Dot Product
A dot product is the outcome of the sizes of two vectors (say A and B) and the cosine of the angle that forms at their point of contact. Suffice it to say that it is a scalar quantity, meaning that the outcome has no direction.
To get the value, you have to find the cosine of the angle formed, allowing the vectors to align in the same direction. You can also use it to obtain the projection of the entities in question. The formula is given as A.B = IAI x IBI x cos (Ɵ). Where A.B means dot product, IAI is the length of A, and IBI is the length of B.
Moving on, it is crucial to point out that the laws it obeys. These laws include cumulative law, distributive law, and scalar multiplication law. More importantly, it is an important tool for determining the magnitude of the points along the angled plane and calculating the projection of a point when the coordinates are given. Before breaking down the difference between cross product and dot product, you have to understand what the former entails.
Definition of Cross Product
Cross product is the outcome of the sizes of two vectors (say A and B) and the sine of the angle that forms at their point of intersection. It is also known as a directed area or vector product. In this case, it is a vector quantity, meaning that the outcome has both size and direction. The resultant vector in this case is perpendicular to the distances in question. The formula is given as AxB = IAI x IBI x sin (Ɵ).
Where AxB means resultant value or cross product, IAI is the length of A, and IBI is the length of B. Just before applying the formula, one has to obey certain rules. These include:
W x Y = Z, W x Z =Y, and Y x Z = W.
Where W, Y, and Z are the unit vectors in 3 different directions.
In other words, a cross product follows distributive law, anti-commutative, and sticks to scalar multiplication law. It can be used to determine the distance along two skew lines as well as to find out if the entities are coplanar.
Main Differences Between Dot Product vs Cross Product
The table below explains cross product vs dot product in detail.
|Basis of Comparison||Dot Product||Cross Product|
|Meaning||The outcome of the lengths of distances and the cosine of the angles they form||The outcome of the lengths of distances and the sine of the angles they form|
|Formula||A.B = IAI x IBI x cos (Ɵ)||AxB = IAI x IBI x sin (Ɵ)|
|Nature of resultant||The resultant is a scalar quantity||The resultant is a vector quantity|
|Outcome of Orthogonality (forming a 90-degree angle)||It is zero (o) when the lengths are orthogonal||The outcome here is the maximum value when the angle of intersection is zero.|
|Difference in law||Obeys many rules, including commutative law||Although it follows many laws, it does not obey commutative law|
Difference Between Dot Product and Cross Product: Conclusion
In summary, this piece on dot product vs cross product has established the obvious distinctions that they both have. To recap, while the former is a scalar quantity while the latter is a vector quantity. There are also other distinctions between them.
However, the resultant is the most significant among all of them. Finally, you need to know this distinction like the back of your hand as a science student, so this tutorial has helped you simplify the ambiguity between them.