Addition of vectors by Head to Tail method (Graphical Method)

Head to Tail method or graphical method is one of the easiest method used to find the resultant vector of two of more than two vectors.
	DETAILS OF METHOD
	Consider two vectors  and  acting in the directions as shown below:
	In order to get their resultant vector by head to tail method we must follow the following steps:
	STEP # 1
	Choose a suitable scale for the vectors so that they can be plotted on the paper.
	STEP # 2
	Draw representative line  of vector
	Draw representative line  of vector  such that the tail of  coincides with the head of vector .
	STEP # 3
	Join 'O' and 'B'.  represents resultant vector of given vectors  and  i.e.
	STEP # 4
	Measure the length of line segment  and multiply it with the scale choosen initially to get the magnitude of resultant vector.
	STEP # 5
	The direction of the resultant vector is directed from the tail of vector  to the head of vector .

MULTIPLICATION & DIVISION OF VECTOR BY A NUMBER (SCALAR)

MULTIPLICATION OF A VECTOR BY A SCALAR
When a vector is multiplied by a positive number (for example 2, 3 ,5, 60 unit etc.) or a scalar only its magnitude is changed but its direction remains the same as that of the original vector. If however a vector is multiplied by a negative number (for example -2, -3 ,-5, -60 unit etc.) or a scalar not only its magnitude is changed but its direction also reversed.
The product of a vector by a scalar quantity (m) follows the following rules:
	(m)  = (m) which is called commutative law of multiplication.
	m(n) = (mn) which is called associative law of multiplication .
	(m + n) = m+ n which is called distributive law of multiplication .
	DIVISION OF A VECTOR BY A SCALAR
	The division of a vector by a scalar number (n) involves the multiplication of the vector by the reciprocal of the number (n) which generates a new vector.
	Let n represents a number or scalar and m is its reciprocal then the new vector  is given by :
	where m = 1/n
	and its magnitude is given by:
	The direction of  is same as that of if (n) is a positive number.  The direction of  is opposite as that of if (n) is a negative number.

Nomenclature of Simple Alkene Chain Molecules

Simple Alkene Chains

An alkene is a molecule made up entirely of carbon and hydrogen where on or more carbon atoms are connected by double bonds. The general formula for an alkene is CnH2n where n is the number of carbon atoms in the molecule.

Alkanes are named by adding the the -ene suffix to the prefix associated with the number of carbon atoms present in the molecule. A number and dash before the name denotes the number of the carbon atom in the chain that begins the double bond.
For example: 1-hexene is a six carbon chain where the double bond is between the first and second carbon atoms.

Click image to enlarge the molecule.

Ethene

Todd Helmenstine

Number of Carbons: 2
Prefix: eth- Number of Hydrogens: 2(2) = 4
Molecular Formula: C2H4

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Propene

Todd Helmenstine

Number of Carbons: 3
Prefix: prop- Number of Hydrogens: 2(3)= 6
Molecular Formula: C3H6

Butene

Todd Helmenstine

Number of Carbons: 4
Prefix: but- Number of Hydrogens: 2(4) = 8
Molecular Formula: C4H8

Pentene

Todd Helmenstine

Number of Carbons: 5
Prefix: pent- Number of Hydrogens: 2(5) = 10
Molecular Formula: C5H10

Hexene

Todd Helmenstine

Number of Carbons: 6
Prefix: hex- Number of Hydrogens: 2(6)= 12
Molecular Formula: C6H12

Heptene

Todd Helmenstine

Number of Carbons: 7
Prefix: hept- Number of Hydrogens: 2(7) = 14
Molecular Formula: C7H14

Octene

Todd Helmenstine

Number of Carbons: 8
Prefix: oct- Number of Hydrogens: 2(8) = 16
Molecular Formula: C8H16

Nonene

Todd Helmenstine

Number of Carbons: 9
Prefix: non- Number of Hydrogens: 2(9) = 18
Molecular Formula: C9H18

Decene

Todd Helmenstine

Number of Carbons: 10
Prefix: dec- Number of Hydrogens: 2(10) = 20
Molecular Formula: C10H20

Isomer Numbering Scheme

These three structures illustrate the numbering scheme for isomers of alkene chains. The carbon atoms are numbered from left to right. The number represents the location of the first carbon atom that is part of the double bond.
In this example: 1-hexene has the double bond between carbon 1 and carbon 2, 2-hexene between carbon 2 and 3, and 3-hexene between carbon 3 and carbon 4.
4-hexene is identical to 2-hexene and 5-hexene is identical to 1-hexene. In these cases, the carbon atoms would be numbered from right to left so the lowest number would be used to represent the molecule's name.