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.
