1. SCALAR (DOT) PRODUCT PERPENDICULAR VECTORS

2. Vectors need to be tail to tail for dot product, vector projections and angle between two vectors as in the diagram.
Example

3. Properties of scalar product.
Scalar product of two perpendicular vectors.

5. Direction cosines.

6. Example

7. Vector resolutes (projections).

8. The shortest distance from point B to the line through OA.

9. Example 3
Given A (2, -1, 2) and B (3, 0, -4), find: a)
b) whether angle AOB is acute, obtuse or right angle
c) the vector resolute of in the direction of
d) the magnitude of angle OAB, to the nearest degree.
, where M is the midpoint of AB.
the shortest distance between O and AB, correct to 1 d.p.
p, given that and are linearly dependent.

11. is the required vector resolute

12. d) is the angle between and .
f) shortest distance is the length OV.

13. g) linearly dependent means that

14. Notes pages for vector resolutes on TI Nspire CAS

15. Notes pages for vector resolutes on TI Nspire CAS
Ex 2C Q2, 3b, 4c,d, 5a, b, 6, 8, 9, 10
Ex 2D Q 1, 3, 4c, 6 c, 7, 9, 10