SS1 Second Term Further Mathematics Lesson Note – Vector II

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WEEK 5

TOPIC:   VECTOR 2

CONTENT:

1. Scalar multiplication of vectors
2. Unit vector
3. Direction cosines
4. Scalar (dot) product: Application of scalar (dot) product.
5. Projections of vectors
6. 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

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