vectors a quantity which has both magnitude and direction is called a vector. vector notations a b a...

Vectors A quantity which has both magnitude and direction is called a vector. Vector notations A B a AB = a AB 4 3 x y x and y are the components of vector AB. P Q b Equal vectors AB = PQ They have the same magnitude and the same direction.

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VectorsA quantity which has both magnitude and direction is called a vector.

Vector notations

Ba AB = a

AB 43 xy

x and y are the components of vector AB.

Equal vectorsAB = PQ

They have the same magnitude and the same direction.

Page 2: Vectors A quantity which has both magnitude and direction is called a vector. Vector notations A B a AB = a AB x and y are the components of vector AB

Addition and subtraction of vectors

P+Q

P 33

Q 52

P+Q 3 5 83 2 1

Page 3: Vectors A quantity which has both magnitude and direction is called a vector. Vector notations A B a AB = a AB x and y are the components of vector AB

Addition and subtraction of vectors

P 33

Q 52

P-Q 3 5 23 2 5

-Q

P-Q

Page 4: Vectors A quantity which has both magnitude and direction is called a vector. Vector notations A B a AB = a AB x and y are the components of vector AB

Scalar multiplication

a 31

b 93

b = 3a

c 62

c = -2a

Page 5: Vectors A quantity which has both magnitude and direction is called a vector. Vector notations A B a AB = a AB x and y are the components of vector AB

Example

A B C D E

F G H I J

K L M N O

P Q R S T

The diagram shows four sets of equally-spaced parallel lines.

Given that and that AB a

AK b

Express the following vectors in terms of a and b.

( i ) BA

( ii ) AH

( iii ) EM

( iv ) LJ

( v ) TA

( i ) a 122( ii ) a b 2( iii ) b a 1

23( iv ) a b 32 4( v ) ( b a )

Page 6: Vectors A quantity which has both magnitude and direction is called a vector. Vector notations A B a AB = a AB x and y are the components of vector AB

ExampleGiven that vectors a and b are not parallel, state whether or not each of the following pairs of vectors are parallel.

2 5( i ) a and a 3 5 15( ii ) ( a b ) and ( a b )

23 2 6( iii ) ( a b ) and ( a b ) 1 1

3 22 3( iv ) ( a b ) and ( a b )

252 5( i ) parallel , a ( a )

( ii ) not parallel

( iii ) not parallel

1 13 22 3 6( iv ) ( a b ) ( a b )

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