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Vectors

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Vectors

- Describes the motion of an object
- A Vector comprises
- Direction
- Magnitude

- We will consider
- Column Vectors
- General Vectors
- Vector Geometry

Size

NOTE!

Label is in BOLD.

When handwritten,

draw a wavy line

under the label

i.e.

a

Vector a

2 up

4 RIGHT

COLUMN Vector

b

Vector b

2 up

3 LEFT

COLUMN Vector?

n

Vector u

2 down

4 LEFT

COLUMN Vector?

b

a

d

c

F

B

D

E

G

C

A

H

k

k

k

k

A Vector has BOTH a Length & a Direction

All 4 Vectors here are EQUAL in Length and

Travel in SAME Direction.

All called k

k can be in any position

k

Line CD is Parallel to AB

B

CD is TWICE length of AB

D

A

2k

Line EF is Parallel to AB

E

EF is equal in length to AB

C

-k

EF is opposite direction to AB

F

k

B

D

2k

F

G

½k

1½k

E

C

-2k

A

H

B

k

D

A

C

C

B

A

Q

P

R

a

b

O

Consider this parallelogram

Opposite sides are Parallel

OQ is known as the resultant of a and b

- Is the same, no matter which route is followed
- Use this to find vectors in geometrical figures

.

Q

S

S is the Midpoint of PQ.

Work out the vector

P

R

a

b

O

= a + ½b

.

Q

S

S is the Midpoint of PQ.

Work out the vector

P

R

a

b

O

- ½b

= b

+ a

= ½b + a

= a + ½b

C

p

M

Find BC

=

+

A

q

B

BC

BA

AC

AC= p, AB = q

M is the Midpoint of BC

= -q + p

= p - q

C

p

M

Find BM

=

½BC

A

q

B

BM

AC= p, AB = q

M is the Midpoint of BC

= ½(p – q)

C

p

M

Find AM

+ ½BC

=

A

q

B

AM

AB

AC= p, AB = q

M is the Midpoint of BC

= q + ½(p – q)

= q +½p - ½q

= ½q +½p

= ½(q + p)

= ½(p + q)

C

p

M

Find AM

+ ½CB

=

A

q

B

AC

AM

AC= p, AB = q

M is the Midpoint of BC

= p + ½(q – p)

= p +½q - ½p

= ½p +½q

= ½(p + q)