Magnitude of a Vector: Overview, Questions, Preparation

A vector is a quantity that has both magnitude and direction. Directed line segments represent it on a graph paper. It can also be represented in the component form. In this form, the vector has vector components along different axes separated by addition or subtraction symbols.

What is the magnitude?

Point A from where the vector AB starts is called its initial point, and point B where it ends is called its terminal point. The distance between initial and terminal points of a vector is called the vector’s magnitude (or length), denoted as |AB|.  The arrow indicates the direction of the vector. The magnitude of a vector is purely the value of the vector without taking into consideration the direction. 

Why is magnitude important?  

If vectors have both direction and magnitude, you might be wondering why we need to isolate the magnitude. Let’s take, for example, a vector of displacement. Now while knowing the direction of displacement is important, sometimes we simply need to know the numerical value of displacement. Say you need to calculate the velocity of a car- the displacement suffered by the car upon the time taken will give you the velocity. 

How to calculate the magnitude of a vector?

Consider the origin O(0,0,0) and a point P(x, y,z). A vector OP having O as initial and P as the final point will be the position vector of point P with respect to O. Using the distance formula, the length of OP, i.e. the magnitude of OP is given by:

Vectors is an important topic with a wide array of Math and Physics applications and are taught in detail in class XII Maths. The magnitude of a vector is a significant component of a vector without which one cannot even begin to use or understand vectors. Vector remains immensely useful for higher Mathematics and Physics.

Q: What is a scalar?

Q: What is a vector?

Q: Can we compare scalars and vectors? 

Q: Do vectors have units?

Q: Does direction matter while calculating magnitude?