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## PowerPoint Slideshow about ' Vectors' - tino

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A VECTOR?

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

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

Size

Label is in BOLD.

When handwritten,

draw a wavy line

under the label

i.e.

a

Column VectorsVector a

2 up

4 RIGHT

COLUMN Vector

k

k

k

General VectorsA 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

General Vectors

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

P

R

a

b

O

Vector GeometryConsider this parallelogram

Opposite sides are Parallel

OQ is known as the resultant of a and b

Resultant of Two Vectors

- 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

Alternatively- ½b

= b

+ a

= ½b + a

= a + ½b

p

M

Find AM

+ ½BC

=

A

q

B

AM

AB

AC= p, AB = q

ExampleM is the Midpoint of BC

= q + ½(p – q)

= q +½p - ½q

= ½q +½p

= ½(q + p)

= ½(p + q)

p

M

Find AM

+ ½CB

=

A

q

B

AC

AM

AC= p, AB = q

AlternativelyM is the Midpoint of BC

= p + ½(q – p)

= p +½q - ½p

= ½p +½q

= ½(p + q)

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