[Maths Class Notes] on Magnitude of a Vector Formula Pdf for Exam

Do you want to know how to calculate magnitude? The magnitude formula of a vector can be found out in two aspects. In one instance, the magnitude is computed for a vector when its endpoint is at origin (0,0) while in the other instance, the beginning and ending point of the vector is at definite points (x1, y1) and (x2, y2) respectively. The Formula of Magnitude of a Vector to compute the length for each of the cases is as follows.

Magnitude of a Vector Formula

Vectors in 2D

A vector with starting point at the origin and an ending point at (a, b) is written . Geometrically, a vector is a vector implicated to a directed line segment, while algebraically it is referred to as an ordered pair. A vector can also be 3-dimensional.

Solved Examples Using The Magnitude Math Formula

Example:

Calculate the magnitude of the vector with [overrightarrow{u}]  = (4,6) ?

Solution: 

Given, [overrightarrow{u}] = (4,6)

Use Magnitude Formula,

[|v|=sqrt{x^{2}+y^{2}}]

[|v|=sqrt{4^{2}+6^{2}}]

[|v|=sqrt{16+36}]

|v|= 7.22

 

Example:

Calculate the direction of the vector [overrightarrow{AB}] whose starting point A is at (2,3)(2,3) and the terminal point at B is at (5,8).

The coordinates of the starting point and the ending point are already given.

Substitute them in the formula tanθ = y₂ − y₁ /x2 − x1

tanθ = 8 − 3/5 − 2            

=5/3

Calculate the inverse tan,

θ = tan−1(5/3)

≈59°

The vector [overrightarrow{AB}] has a direction of about 59°