1. Scalar Product (Dot product) of vectors:, are vectors and given like that = (x 1,y 1 ) and = (x 2,y 2 ). We can define the scalar product as:. = = x 1.x 2 +y 1.y 2

2. Example: and are vectors. If =16, then find the values of x.

3. Properties of Scalar Product: 1. 2. k 1,k 2 R 3.

4. Angle between two vectors:

5. = | |. | |.cos (angle between two vectors) If Ө=0º, vectors are parallels and at the same direction. =| |.| | If Ѳ =90°, vectors are perpendicular to each other.

6. If the vectors are parallel to each other but at the opposite direction:

7. Example: Evaluate if the angle between and is 60° and |A| = 20 br, |B|=10br.

8. Example: With the given points A(-3,4), B(1,-5), C(4,3) and D(-1,6), what is the scalar product of ?

9. Example: and are givens. If, then find the value of a.

10. Example: Find cosine of the angle between the vectors. A=(-2,1) and B=(2,2).

11. Example: If and are perpendicular to each other. Find the value of m.

12. Example: If the vector and vector are perpendicular to each other, then find the value of m.

13. Example: Find the scalar product of the vectors and

14. Example: The triangle in the figure is an isosceles right triangle. If |AE|=|DC| = 2br and |EB|=3 br. Then find

15. Example: are vectors. If, then find the value of x.