Basics of Percent Error & Cross Product in Mathematics

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Do you know the importance of estimates i.e. percent error or cross product in mathematics? This is important not only for mathematics but for other subjects also. There are certain chances of correctness in every situation. The situation may be any condition or any question.

Let’s see if you have a box full of candies and don’t know how many candies are there in the box. What will you do? You will definitely try to estimate the candies. You will try to make your best-estimated guess to know how many candies are there. 

You can win the prize if you make your estimated closet to the actual amount of candies. This can be known by the per cent error. There you will know about the basic overview of percent error & how to calculate cross product in mathematics.

What is the Percent Error?

Percent error is the difference between the exact and estimated values. This is expressed as a percentage of the exact error. The error is expressed as a percentage because this creates the difference between the actual and approximate value. 

This is used in many conditions. It has extensive use in math, science, and statistics. You can use this to measure the difference in the calculated value and the value which you have is used as an experimental value. This helps you to get to know about the exact value. 

Percentage Error Formula:

Here, you will see and know about the formula which is used to measure the percentage error. To know the formula you need to know that it is the difference between the expected or experimental value and actual or exact value, which will then divided by the known value. Then multiply them with 100%. 

This is got to know that mostly the percent error will express as a positive value. If you see the negative value, ignore the negative sign. You need to divide the absolute value by the actual value. Then this will know as a percentage value. 

Accepted value – experimental value / accepted value x 100%

For Example:

If you want to know how big or great your error is, you need to know about the percentage error because this will help you to know your correct analysis during any process. Let’s discuss an example to understand the concept properly.

For instance, if you have a problem and you have estimated its correct answer. If you have a 40% error you are totally on the wrong track. But if you have a 1% error instead, you are more close to the true or actual value. 

It means if you have errors that have a smaller percentage then you are close to the original or accepted value. There are some errors about which you cannot estimate properly like, the hand can shake, or you can fall. 

How to calculate the percent error?

There you see some steps to know how to calculate the percent error.

  • First of all, you need to make a difference between two values. Consider making a difference of one value from the other value. You need to know that if you are considering the minus sign then you don’t worry about the order. One thing you must need to know. Always subtract the actual value from the expected value. This value will know as an error.
  • The next step is to you need to perform the division between the actual and expected value.
  • After division, you will receive a decimal number. Now, multiply this decimal number with 100 to create its percentage. 
  • Now, as you have a percentage value, just add the percentage sign % to represent the percent error. 

You may also use the online tool for calculating cross-product online like error percent calculator etc.

What is Cross Product?

Do you know what a vector is? A vector is an object which has both the magnitude and the direction. As a single vector contains both the magnitude and the direction therefore two vectors will multiply by using the process of the cross product.  

If you see the cross product of two vectors a × b, which creates another vector, then it will be the right angle to them. If you see the magnitude, it will be equal to the rectangle with the two vectors. 

In Which Direction the cross product will be?

You will see that the cross product of any vector will be at the right angle but completely in the opposite direction. This seems complex but it can be easily understood by the Right-Hand Rule. This will help you to understand the direction of the vector.

Right-Hand Rule:

You need to point out your right hand in such a manner that your thumb point in the upward direction.  Your index finger will point in the direction of one vector. Now point your middle finger along with the second vector. Make sure to note that the cross product will be in the direction of the thumb.

How to calculate the cross product?

This is crucial to know because it is important for the sum of two vectors. For instance, if you have two vectors a and b or x and y. how will you calculate its cross product? Let’s solve this riddle.

  • |x| will be the magnitude of vector x
  • |y| will be the magnitude of vector y
  • θ will be the angle between x and y
  • n will be the unit vector of both vectors x and y at the right angles
  • So, the magnitude is the magnitude of x and the magnitude of y. this will be equal to the sine angle, which falls between the x and y vector.
  • At the final step, you need to multiply them with the n vector to make it heads in the correct and right-angled direction for both vectors x and y.

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Difference B/w Cross Product & Percent Error

if we talk about the differences between these two concepts of cross-product multiplication and percentage error, then we will find a huge difference between them.

The percentage error is the kind of error of the difference of actual value from its standard value. There is some true value that is precisely taken and recorded as a standard. The percentage error value contains the comparison between that standard true value and the observed value that is measure by any individual. The percentage error might be positive or negative depending upon the observed value.

If the observed value will greater than the true value, then it will generate a negative percent error. While, if the observed value will be less than the true value, then it will surely generate a positive error in our measurement.

On the other hand, If we go toward the cross product of the point, Then it is too different to that concept. Cross product is the multiplication of two-point which contains the scalar multiplication as well as the direction in which these vectors are moving.

Conclusion

Here, we have discussed the basic overview of percent error & cross product in mathematics. This is important to know about both concepts.

Percent error will help you to understand the concept of error and correctness. Cross product will help you to understand the direction and angle of the vector basic overview of percent error & cross product in mathematics.

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