To find the magnitude (length) of a vector in 2D or 3D, one uses the formula that takes the square root of the sum of the squares of the vector's components. For a vector a with components a1, a2, and a3, the magnitude is calculated as the square root of a1^2 + a2^2 + a3^2. The magnitude of a vector is denoted by |a|.

1. Finding the Magnitude of a Vector in 2D and 3D
Given the position vector a = !
!
find the magnitude of the vector.
If we have the vector a = !
!
how do we find the magnitude (length) of this
vector?
Consider two points A and B such the 𝐴𝐵 looks like this:
Where 𝐴𝐵 =
!
!
!
Find the magnitude of this vector
x
y
To find the magnitude of a vector a = !!
!
! we use the formula:
We use the notation |𝒂| to say the magnitude of vector a.
A
B
6
3
1
To find the magnitude of a vector a = !!
!
!
! we use the formula:
We use the notation |𝒂| to say the magnitude of vector a.