math unit38 vectors
TRANSCRIPT
Unit 38Vectors
Presentation 1 Equal Vectors Presentation 2 ComponentsPresentation 3 Vector ExpressionsPresentation 4 Addition and Subtraction of VectorsPresentation 5 Vector Geometry 1Presentation 6 Vector Geometry 2
Unit 3838.1 Equal Vectors
In the following diagram, stateWhich 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 directionsc and b e and j?
???
?
Unit 3838.2 Components
Does ?
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Given that , , calculate
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No
Unit 3838.3 Vector Expressions
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
?
Unit 3838.4 Addition and Subtraction of
Vectors
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
ba
(iv) a + c - b
a + c - b
Unit 3838.5 Vector Geometry 1
Express, in terms of u and v,(a)(b)(c) , where M is the midpoint of AC, ?
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Express, in terms of u and v,(d)(e) , where N is the midpoint of BD,(f)
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?
? ?
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What can you deduce about points M and N? They are coincident.
Hence and
Unit 3838.6 Vector Geometry 2
(a) Express in terms of x and y,(i) (ii) (iii)
Solution
In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that
(i)
(ii)
(iii) ??
?
?
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In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that
(b) Show that Solution
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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?
?
??
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from part (b)
from part (a)