M2.1 Vector Calculus Introduction

Scalars: The physical quantities having only magnitude are called as scalars. Ex: length, mass, time, speed, \(a=4, c=\pi\)
Vectors: The physical quantities having both magnitude and direction are called as vectors. Ex: velocity, force, \(\vec{v}=a \hat{i}+b \hat{j}\) A vector in three dimension is of the form \(\vec{v}=a\hat{i}+b \hat{j}+c \hat{k}\), where \(\hat{i},\hat{j}, \hat{k}\) are the unit vectors in the direction of \(X, Y\) and \(Z\) respectively.
Addition of two vectors
Let \(v_1=a\hat{i}+b \hat{j}, v_2=c\hat{i}+d \hat{j}\) then \(v_1+v_2=(a+c)\hat{i}+(b+d) \hat{j}\) and \(v_1-v_2=(a-c)\hat{i}+(b-d) \hat{j}\)
Following is the example for vector addition, created using geogebra.

u(Green)=v1(Blue)+v2(Red)