how to find the magnitude of a vector with examples
How to Find the Magnitude of a Vector (with Examples)
To find out the value of any given vector component, it is necessary to find out its direction as well as magnitude. We, at Buzzle, have described the method to calculate the magnitude of a given vector.
Did You Know?
The vector with magnitude equal to 1 is known as a unit vector.Notation
The notation for magnitude of a vector is two vertical bars.
| x |
To avoid confusion with absolute value, the magnitude X can also be written as;
|| x ||
However, the double bar notation is not used frequently.
Formula
The magnitude of a vector, v = (x,y), is given by the square root of squares of the endpoints x and y.
| v |
=
| √ | x2 + y2 |
| v |
=
| √ | (x2 - x1) 2 + (y2 - y1)2 |
Calculate magnitude of vector a = (4, 3).
Thus, the magnitude of vector a(4, 3) is 5 units.
| a |
=
| √ | 4 2 + 32 | ||
| √ | 16 + 9 | ||
| √ | 25 | = | 5 |
Calculate magnitude of vector b = (-3, 5).
Thus, the magnitude of vector b(-3, 5) is 6 units.
| b |
=
| √ | (-3) 2 + 52 | ||
| √ | 9 + 25 | ||
| √ | 36 | = | 6 |
Vector Magnitude in Space
The aforementioned examples are for the vectors in 2D form. However, if you have to calculate vector magnitude in 3D space, you cannot use this formula. To calculate magnitude of u(x1, x2, x3), the correct formula is;
| | u | = | √
|
| v |
=
| √ | (x2 - x1) 2 + (y2 - y1)2 + (z2 - z1)2 |
Calculate the magnitude of vector c = (2,5,3).
The magnitude of vector c is 6.16 units.
| c |
=
| √ | 22 + 52 + 32 | ||
| √ | 4 + 25 + 9 | ||
| √ | 38 | = | 6.16 |
Calculate the magnitude of vector u = (-1,1,2).
Thus, the magnitude of the given vector is 2.44 units.
Calculate magnitude of vector with co-ordinates A(2,3,4) and B(-1,3,-2).
| u |
=
| √ | (-1)2 + 12 + 22 | ||
| √ | 1 + 1 + 4 | ||
| √ | 6 | = | 2.44 |
| u |
=
| √ | (-1-2)2 + (3-3)2 + (-2-4)2 | ||
| √ | 9+ 0+ 36 | ||
| √ | 45 | = | 6.7 |