COLLINEAR AND COPLANAR VECTORS
1. COLLINEAR VECTOR
These are vectors having the same slope (re direction).
Pg. 10 drawing
= μ 
= t 
Where
Æ›, μ and t are scalar
Again 
and 
to be collinear 
x 
= 0
2. COPLANAR VECTOR
These are vectors which lie on the same plane
Eg. Pg. 10 drawing
For the vectors
, 
and 
to be coplanar
= 0
= 0
= 0
Generally
= 
= 
= 0
Question
31. Given that
= 3
+ 4
32. Find the value are collinear vectors 2
– 
+ 
, 
+ 2
+ 3
and 3
+ 
+ 5
are coplanar.
33. Find unit vector in the direction of 
= 6
+ 3
+ 
and state its length
LINEAR COMBINATION OF VECTORS
Suppose that 
are vectors and
, β and γ are real numbers (sealers). Then a vector 
= 
+ β 
+ γ 
is a linear combination of vectors 
NB
To solve vectors means to put the vectors into linear form
Question
34. If 
= 
+ 
, 
= 
– 
and 
= 3
– 4
resolve 
into vectors parallel to 
35. Express the vector r = 10
– 3
– 
as a linear function of 
given that
= 2
– 
+ 
= 3
+ 2
– 
and
= –
+ 3
– 2
Note: Required to be placed in a right position
Subtopic: Dot Product
Proving cosine rule using dot product
Consider the triangle ABC above
Subtopic: Cross Product
Proof of sine rule Consider the ∆ABC with sides A,B and C respectively
Construct a line AH which lies on BC and perpendicular.
Equating area
