The content is just an excerpt from the complete note for SS1 Second Term Further Mathematics Lesson Note – Vector II. Check below to download the complete DOCUMENT
WEEK 5
TOPIC: VECTOR 2
CONTENT:
- Scalar multiplication of vectors
- Unit vector
- Direction cosines
- Scalar (dot) product: Application of scalar (dot) product.
- Projections of vectors
- Application of scalar product
Sub-Topic: VECTOR MULTIPLICATION BY A SCALAR/UNIT VECTOR
Let say and m are scalars then the following laws are true for any vectors a and b:
a is also a vector
(a+ b) = a + b (distributive)
( + m)a = a + ma.
If k is a scalar, then ka is a vector which is parallel to a but k times the magnitude of a. If k>0 then ka is in the same direction of a.
However, if k<0, then ka is in a direction opposite to a
THE UNIT VECTOR
The unit vector is an important concept in the study of vectors.
The definition of unit vector was given earlier as a vector which has an absolute value of unity
We now amplify on this concept.
If OP = ai + bj, then we represent a unit vector in the direction of p by . since a unit vector has a magnitude equal to unity
To gain full access to the note: DOWNLOAD FILE
