1. Vectors The modulus of a vector is its magnitude.
The modulus of a is written as .
The modulus of is written as
Unit vectors are vectors with unit magnitude.
is the unit vector in the direction of a.
i, j and k are unit vectors parallel to the axes
Ox, Oy and Oz
Position vector and its magnitude
Displacement vector

2. Vectors
Example
The points A, B and C have coordinates (4, -2), (3, 3) and (-2, 1) respectively and O is the origin.
Find in terms of i and j , the vectors
Parallel vectors
is parallel to
and is s times its length.

3. Unit vectors Magnitude of a vector Example
Find the magnitude of each these vectors
Unit vectors in these directions are

4. Example
Find a vector of magnitude 30 in the direction of 6i -8j
Example
p = 4i + j
q = 6i - 5j
r = 3i + 4j
Find numbers m and n such that mp + nq = r.
i component:
4m + 6n = 3
[1]
j component:
m - 5n = 4
[2]
[1] – 4[2]:
26n = - 13
 n = - ½
m = 1.5

5. Example
Find
the vector AB
AB
(iii) Position vector of the mid-point of AB
(i)
(ii)
(iii)

6. Example
Given that v = i +2j – 6k, find  such that v= 7
Example
v1 = 3i + 2j – k, r2 = 2i – k. Find the unit vector in the direction of 2v1 – v2.
The length of 2v1 – v2 =