What is magnitude of vector

The magnitude of a vector formula helps to summarize the numeric value for a given vector. A vector has a direction and a magnitude. The individual measures of the vector along the x-axis, y-axis, and z-axis are summarized using this magnitude of a vector formula. The magnitude of a vector is always a positive number or zero, i. Let us understand the magnitude of a vector formula using a few solved examples in the end.

For a given vector with direction ratios along the x-axis, y-axis, and z-axis, the magnitude of the vector is equal to the square root of the sum of the square of its direction ratios. This can be clearly understood from the below magnitude of a vector formula.

The starting and ending point of the vector is at certain points x 1 , y 1 and x 2 , y 2 respectively. This formula is derived from the Pythagorean theorem. Let us see the applications of the magnitude formula in the following section.

The magnitude of a vector formula summarizes the numeric value for a given vector. The magnitude of vector formulas are as follows:. The magnitude of a vector refers to the length or size of the vector. Now, we can add two vectors by simply joining them head-to-tail, refer the diagram given below for better understanding:.

And it doesn't matter in which order the two vectors are added, we get the same result anyway:. Notation :. A vector can often be written in bold, like a or b. We can also subtract one vector from another, keeping the two points given below in our mind:. Firstly, we need to reverse the direction of the vectors we want to subtract, this changes the sign of the vector from positive to negative. Secondly we need to add them as usual:.

As we know, that vector can be defined as an object which has both magnitudes as well as it has a direction. Now if we have to find the magnitude of a vector formula and we need to calculate the length of any given vector. Quantities such as velocity, displacement, force, momentum, etc are the vector quantities. But the quantities like speed, mass, distance, volume, temperature, etc. The scalar quantities are the ones that have the only magnitude whereas vectors generally have both magnitude and direction.

The magnitude of a vector formula can be used to calculate the length for any given vector and it can be denoted as v , where v denotes a vector. So basically, this quantity is used to define the length between the initial point and the end point of the vector.