Vectors

Vectors are very important in mathematical computing and in computer graphics .Vector graphics is economical in its use of memory, as an entire line segment is specified simply by the coordinates of its endpoints. A vector can be represented by an arrow whose length represents the magnitude and the direction represents the vector direction.

The above vector a can be represented as

a = [a1, a2]

The arithmetic operations can be performed in the following way:

o Addition

If a and b are two vectors

a = [a1, a2]

b = [b1, b2]

then the sum of a and b is

a + b = [a1+b1 , a2+b2]

o Subtraction

If a and b are two vectors

a = [a1, a2]

b = [b1, b2]

then the difference of a and b is

a - b = [a1-b1 , a2-b2]

o Multiplication

If a and b are two vectors

a = [a1, a2]

b = [b1, b2]

then dot product of a and b is

a . b = (a1 * b1 ) + ( a2 * b2)

o Length of vector

If a is a vector

a = [a1, a2]

then the length of vector a is

length =

Assignment

Write a C++ program that performs the above mentioned operations on vectors with the help of above mentioned formulae. The program should have four user defined functions for the above operations.

1) Addition

2) Subtraction

3) Multiplication

4) Length

The following menu of commands should be displayed at the start of program execution.

Press 'a' to add two vectors

Press 's' to subtract two vectors

Press 'm' to multiply two vectors

Press 'l to calculate the length of vector

Press 'q' to quit

Please enter your choice: a

After the user selects a choice, prompt the user to enter the vector components on which the selected mathematical operation is to be performed, and then display the result. For example,

if the user enters a then your output should be:

Enter first component of vector : 2

Enter second component of vector : 7

The vector is : [ 2 , 7 ]

Enter first component of vector : 6

Enter second component of vector : 3

The vector is : [ 6 , 3 ]

The sum is [ 8 , 10 ]

if the user enters s then your output should be :

Enter first component of vector : 2

Enter second component of vector : 7

The vector is : [ 2 , 7 ]

Enter first component of vector : 6

Enter second component of vector : 3

The vector is : [ 6 , 3 ]

The difference is [ -4 , 4]

if the user enters m then your output should be :

Enter first component of vector : 2

Enter second component of vector : 7

The vector is : [ 2 , 7 ]

Enter first component of vector : 6

Enter second component of vector : 3

The vector is : [ 6 , 3 ]

The multiplication is 33

After the menu if the user selects l then your output should be

Enter first component of vector : 1

Enter second component of vector : 2

The vector is : [ 1 , 2 ]

The length is 2.23607

After the menu if the user selects q then your output should be

Press any key to continue ..

Conditions that must be checked and fulfilled:

1) If a user enters choice other then choices given in menu, then a message should be displayed You have entered wrong choice: and main menu should be displayed again.

2) If a used enters a ,s or m then you have to take components of two vectors then do calculation on them

3) If a user enters l then you have to take components of one vector only then do calculation on it.