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Vectors
Basic of a Vector
A directed quantity, one with both magnitude and direction are called Vectors
...


 Geometric Representation of a Vector
There are 3 steps to geometrically draw a vector
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The line should be parallel to the direction of the vector
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The line should be proportional to the size of the vector
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Put an arrow head to point the direction of the vector
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1
...
Then the arrow head points from A end to B end, we numbered those as
⃗⃗⃗⃗⃗
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3
...

Example:
,
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H
...
R
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𝐵
⃗⃗⃗⃗⃗ =
𝑎

𝐴

 Unit Vectors ( )

A vector is referred to as a unit size in any direction
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Example: To direct ⃗⃗⃗⃗⃗ ,
⃗⃗⃗⃗⃗⃗⃗

or

⃗⃗⃗⃗⃗

⃗⃗⃗⃗⃗

To direct ,
=

or

 Optical Vector ( )
A vector is referred to as a zero unit size in any direction
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When

is a real scalar,

1) When
If

,
is,
= 2, then

:
like
=2

time big and point to the same direction
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H
...
R
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like – time big and opposite to the same vector

is,

𝐷
𝐵
-2𝑎

AB ∥ CD and CD = 2AB

𝑎
𝐴

𝐶

That means - is a vector that parallel, same proportional and opposite to


...


𝐴

in picture (1), firstly we

Then we join those 2 vectors like picture (2) (direction of arrows should flow
without any opposite turnings)
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⃗⃗⃗⃗⃗ =

+

Also we write this,
If ⃗⃗⃗⃗⃗⃗⃗ =

+ , {⃗⃗⃗⃗⃗

⃗⃗⃗⃗⃗

}

⃗⃗⃗⃗⃗ = ⃗⃗⃗⃗⃗ + ⃗⃗⃗⃗⃗
This is the Triangle law of vector addictive
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H
...
R
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−

-𝑏

⇛

𝑎

𝑎
𝑎− 𝑏

⇛

-𝑏

𝑎

Vector Additive Theories :
When
are any kind of vectors, and and
3 main theories
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Commutative Law

2
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Distributive Law
(

)

(

)

Example :

When
⃗⃗⃗⃗⃗

, , are distinct points and ⃗⃗⃗⃗⃗

, ⃗⃗⃗⃗⃗

then show the result of

–
...
H
...
R

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