Magnitude — Precalculus, what it means and where it is taught
The length of the vector, written |v|.
Taught in Precalculus.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Vector — A quantity with both magnitude and direction.
Practise this idea
8 questions in the course bank use Magnitude, in Exponential & Logarithmic Models, Vectors.
Problem 1
A magnitude 8 earthquake releases how many times the energy of a magnitude 6?
- About 1000
- About 2
- About 100
- About 32
Worked answer
About 1000
Two steps
32 × 32 ≈ 1000
Problem 2
Find the magnitude of ⟨ 3, 4 ⟩.
Worked answer
5
√9+16 = 5
Problem 3
Find the magnitude of ⟨ -8, 6 ⟩.
Worked answer
10
√64+36 = 10
Problem 4
Find the magnitude of 3⟨ 1, 0 ⟩.
Worked answer
3
⟨ 3, 0 ⟩ has length 3
Problem 5
A vector has magnitude 10 at 30°. Find its horizontal component.
Worked answer
5sqrt(3)
x
=
r
\
c
o
s
\
t
h
e
t
a
.
Problem 6
A vector has magnitude 10 at 30°. Find its vertical component.
Worked answer
5
10sin 30° = 5
Problem 7
Two forces, 12 N east and 5 N north, act on a point. Find the magnitude of the resultant.
Worked answer
13
√144+25 = 13
Problem 8
Find the magnitude of the unit vector in the direction of ⟨ 6, 8 ⟩.
Worked answer
1
Dividing by the magnitude 10 gives ⟨ 0.6, 0.8 ⟩
Its length is 1 by construction