Math unit38 vectors
Download as PPT, PDF0 likes150 views
This document contains 6 presentations on vectors: 1) Identifying equivalent and opposite vectors in a diagram 2) Calculating components of vectors 3) Writing vector expressions in terms of other vectors 4) Illustrating vector addition and subtraction on a grid 5) Expressing vectors in terms of other vectors using properties of midpoints 6) Expressing vectors in terms of other vectors and proving collinearity using properties of parallelograms
Math unit38 vectors
- 1. Unit 38 Vectors Presentation 1 Equal Vectors Presentation 2 Components Presentation 3 Vector Expressions Presentation 4 Addition and Subtraction of Vectors Presentation 5 Vector Geometry 1 Presentation 6 Vector Geometry 2
- 2. Unit 38 38.1 Equal Vectors
- 3. In the following diagram, state Which pairs of vectors are equivalent and which pairs of vectors are opposite directions Equivalent vectors: a and b b and i f and g Vectors in opposite directions c and b e and j? ??? ?
- 5. Does ? ? ? ? ? Given that , , calculate ? ? ? ? ? ? No
- 6. Unit 38 38.3 Vector Expressions
- 7. Write down each of the following in terms of d and/or e. (a) (b) (c) ? ?? ?? Mark clearly on the diagram (a) the point P such that (b) the point Q such that Q P ?
- 8. Unit 38 38.4 Addition and Subtraction of Vectors
- 9. Given that On the grid below, illustrate the following vectors (i) b – c (ii) c + a (iii) a + b (iv) a + c – b b - c - c b (i) (ii) c + a c a (iii) a + b b a (iv) a + c - b a + c - b
- 10. Unit 38 38.5 Vector Geometry 1
- 11. Express, in terms of u and v, (a) (b) (c) , where M is the midpoint of AC, ? ? ?
- 12. Express, in terms of u and v, (d) (e) , where N is the midpoint of BD, (f) ? ? ? ? ?
- 13. What can you deduce about points M and N? They are coincident. Hence and
- 14. Unit 38 38.6 Vector Geometry 2
- 15. ) Express in terms of x and y, (i) (ii) (iii) olution In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that (i) (ii) (iii) ? ? ? ?
- 16. ? In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that (b) Show that Solution ?
- 17. In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that (c) Given that E is the midpoint of DC, prove that A, P and E are collinear. Solution so Hence A, P and E are collinear? ? ?? ? from part (b) from part (a)