Vector — Precalculus, what it means and where it is taught
A quantity with both magnitude and direction.
Taught in Precalculus.
Where it is taught
What uses it later
This idea is needed for:
- Magnitude — The length of the vector, written |v|.
- Component form — A vector written as its horizontal and vertical parts, ⟨ a, b ⟩.
- Resultant — The single vector that two or more vectors add up to.
Practise this idea
4 questions in the course bank use Vector, in Vectors.
Problem 1
For the same vectors, find the second component of u+v.
Worked answer
6
1+5 = 6
Problem 2
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 3
A vector has magnitude 10 at 30°. Find its vertical component.
Worked answer
5
10sin 30° = 5
Problem 4
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