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)