Tools have revolutionized the world and made our daily work more effective and competitive.

Different tools make the calculation more easy and more convenient for us. Solving a quadratic equation and finding a dot product of two or more than two vectors can sometimes be really challenging. But with the development of technology, we don’t have to do it step by step; we can easily calculate these things with handy tools or calculators in just one click. Before discussing the features of these calculators, let’s have a brief view of what are “quadratic equation” and “dot product of vectors”?

Quadratic Equation

An equation that contains the square of the unknown (variable) quantity but no higher power is called a quadratic equation or an equation of the second degree.

We can also say that the second-degree equation in one variable x is ax²+ bx +c = 0 where a≠0 and a, b, c are real numbers. This equation is also called the general or standard form of a quadratic equation.

Quadratic Formula

x=−b±√b2–4ac/2a. is called a quadratic formula. Quadratic Equations can be solved with the help of this formula. The equation must be in this form: ax²+ bx +c = 0.

Quadratic Calculator

This calculator will save a lot of your time, whether you are a student who wants to solve an algebraic problem or a professional who wants the solution in one click.

The specific Quadratic Calculator calculator works on the algorithm of the quadratic formula. What you have to do is provide the value of a, b and c, and you can get the roots of the equation in one click.

This tool not only provides you with the roots but it can also be used to determine the nature of the roots of the equation that lies with the axis.

The nature of the roots can be real, unequal, rational, irrational and imaginary.

The quadratic equation has applications in different fields, from finance to physics. Quadratic Equations are applicable in different areas like Structural Design, economic relationships like supply and demand, profit analysis, financial investments, computer animation, projectile motion, optimization problems and for describing shapes of certain lenses.

Dot product

There are two types of vector multiplications. The product of these two types is known as scalar product and vector product.

If the product of two vector quantities is a scalar quantity, then it is called a scalar or dot product.

And if the product of two vector quantities is a vector quantity, then it is called a vector or cross product.

The dot product of two vectors, A and B, is written as 

 A.B = |A|.|B| cosθ

here, A and B are the magnitude of vectors A and B, while θ is the angle between them.

The simplest example of a dot product is the product of force and displacement that is equal to work done.

 F.D = FD cosθ= work done

Dot products are also used to calculate work done and determine the angle between vectors. The dot product is also used to calculate the torque, lighting effects, shadows, reflections, and intensity of light hitting the surface. It is also used to calculate the projection of a vector on the other vector.

Dot Product Calculator

With the increase in development in science and technology, there are calculators through which we can easily calculate the dot product of different vectors. What you have to do is provide the components of your vector, and the calculator will show you the result.

The dot product of any two vectors obeys commutative law, e.g.,

A.B = B.A

This  Dot Product Calculator is really useful for physicists, engineers and any person who is working with vector quantities.

Conclusion

In the fast and furious world, no one wants to spend time on long calculations that can be done with just one click. Using Calculators for finding the roots of quadratic equations and for the dot product of two or more two vectors is really a great idea. It saves your time and also makes your calculation error humanely possible and mistake-free. You can easily do these complex calculations in no time. These tools are helpful for students and for real life problem solvers also.