Vector

Introduction:

    Introduction to vectors is nothing but we are going to learn about the basic things in the vectors. In vectors the basic thing is operations of vectors. So we are going to learn this in the introduction. Basically vector is a combination of direction and magnitude. We can perform all the arithmetic operations in vectors. We will see some example for vectors in the introduction

                                   `p vecx + q vec y + r vecz`

                 This is one of the examples for vector. Here p, q, and r are the magnitude of the vectors.

Introduction to Vector Operations:

          We can perform all the arithmetic operations using vectors.
Addition of two vectors:
            Addition of two vectors is like the normal arithmetic operation. We have to add the magnitude of the vectors.
Add the following vectors:
                          ` 5 vecx +6 vecy +9 vecz` And `2 vecx + 3vecy +4 vecz`
Solution:
           If we have to add any two vector then we have to add the magnitude of the given vectors.
                              `5 vecx +6 vecy +9 vecz + 2 vecx + 3vecy +4 vecz`
                                    = `7 vecx + 9 vecy + 13 vecz`
Subtraction of two vectors:
                                 Subtraction of two vectors is nothing but same as the addition.
Perform the subtraction operation of the following vectors:
  ` 4 vecx +2 vecy +8 vecz` And `2 vecx + 3vecy + 4 vecz`
Solution:
            If we want to subtract any two vectors we have to subtract the magnitude alone.
                              `= 4 vecx +2 vecy +8 vecz -(2 vecx + 3vecy +4 vecz)`                                                         
                                `"= 4 vecx + 2 vecy + 8 vecz - 2vecx - 3vecy - 4 vecz `
                                `"= 2 vecx - 1 vecy + 4 vecz `