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Unit 38 Vectors

Unit 38 Vectors. Unit 38. 38.1 Equal Vectors. In the following diagram, state Which pairs of vectors are equivalent and w hich 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. ?. ?.

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Unit 38 Vectors

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  1. Unit 38Vectors

  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 bb andi f and g Vectors in opposite directions c and b e and j ? ? ? ? ?

  4. Unit 38 38.2 Components

  5. Given that , , calculate ? ? ? ? ? ? ? ? ? ? Does ? No

  6. Unit 38 38.3 Vector Expressions

  7. Mark clearly on the diagram (a) the point P such that (b) the point Q such that Q P Write down each of the following in terms of d and/or e. (a) (b) (c) ? ? ? ? ? ?

  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 (i) b - c - c b (iii) (ii) c + a b a c a + b (iv) a 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. Hence and What can you deduce about points M and N? They are coincident.

  14. Unit 38 38.6 Vector Geometry 2

  15. In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that • Express in terms of xandy, • (i) (ii) (iii) • Solution (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 from part (a) ? from part (b) ? Hence A, P and E are collinear ?

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