What is the Dot Product of Perpendicular Vectors?
Problems related to the multiplication of vectors are common in Physics and Mathematics. You may be asked to find the dot product of two vectors in your textbooks or assignments. The questions related to the dot product of perpendicular vectors are the simplest ones when compared to the cross product of the same vector’s type or others.
Are you struggling to understand this multiplication? Read this blog till the end as it will discuss this topic in detail. By the end, you will learn about perpendicular vectors and their multiplication as well as check the solved example related to it.
What are perpendicular vectors?
Two vectors are said to be perpendicular if they are making an angle of 90 degrees with each other. In simple words, if vector A is pointing up along with y-axis and the other vector is pointing horizontally along with x-axis, those vectors are said to be perpendicular.
What is the dot product of two perpendicular vectors?
To learn about the dot product of 2 vectors, you must understand the formula of the dot product of two vectors first. For two vectors, A and B, the dot product formula will be written as:
A . B = AB Cos𝜽
In the above formula, A and B on the left-hand side represent the vectors while “A” and “B” on the right side show the magnitude of the vectors. “𝜽” is the angle between two vectors being multiplied to get the resultant one.
The dot product of two perpendicular vectors is “zero” because the angle between them is “90” degrees. It means there will be no resultant vector when two perpendicular vectors are multiplied.
Why the dot product of perpendicular vectors is zero?
The above formula for the dot product of perpendicular vectors involves “Cos 𝜽” and the value of “Cos 90” is “0”. Resultantly, the resultant of the above formula will become “0” when two perpendicular vectors are multiplied.
If you have other types of vectors and facing problems while finding their multiplication, you can use the dot product calculator. This calculator can assist you in solving your questions quickly to complete your assignment. It shows you a step-by-step solution by following which you can learn the way to find this product easily.
Example of the dot product of 2 perpendicular vectors
example1:
Find the dot product of two vectors having coordinates (2, 3) and (4, 8) while the angle between them is 90 degrees.
Solution:
Suppose the vectors are “A” and “B” with vertices given in the question respectively. By putting the values in the above formula of the dot product,
A . B = AB Cos𝜽
= [(2 x 4) + (3 x 8)] Cos (90)
As,
Cos 90 = 0
So,
A . B = 0
Conclusion
By reading this guide and checking the example, we hope you have learned about the dot product of two perpendicular vectors. If you still have doubts, you can use the dot product calculator to check the solution for your required question and understand its steps.
FAQ
What is the dot product of perpendicular vectors?
The dot product of perpendicular vectors is always “Zero”.
What is the dot product of two perpendicular vectors?
If two given vectors are perpendicular, the dot product of those vectors will be “0” because of the “Cosine” involvement in the formula for angle calculation.
Is the dot product of perpendicular vectors 0?
Yes, the vectors are said to be perpendicular only when their dot product is “0”.
What does a parametric equation show you?
The parametric equation describes the position of the point on the circumference of the circle for which the equation has been written.
What is the dot product of two perpendicular vectors A and B equal to?
The dot product of two perpendicular vectors A and B can be calculated as,
A . B = AB Cos𝜽
