Vector Addition in Component form

Overview

**Vector Addition : Component form**

» individual components add

→ $r}_{x}={p}_{x}+{q}_{x$

→ $r}_{y}={p}_{y}+{q}_{y$

→ $r}_{z}={p}_{z}+{q}_{z$

component form

The component form of a vector is representation of vector with the 'components along $x,y,$ and $z$ axes'.

Two vectors $ai$ and $pi$ are added. The result of addition of the two vectors is $(a+p)i$

*The magnitudes add up as two vectors are in the same direction $i$ , that is, along x-axis.*

The result of addition of two vectors $ai+bj$ and $pi$ is '$(a+p)i+bj$'. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In this problem, in the direction of x-axis, $ai$ and $pi$ are given. They are added in magnitude.

That is expanded further. The result of addition of two vectors $ai+bj+cj$ and $pi+qj+rk$ is '$(a+p)i+(b+q)j+(c+r)k$'. The magnitudes add up along the directions in parallel and the directions in perpendicular are kept separately. In these two vectors, the components along the three axes are given in component form.

summary

**Addition of two vectors: ** When two vectors $\overrightarrow{p}={p}_{x}i+{p}_{y}j+{p}_{z}k$ and $\overrightarrow{q}={q}_{x}i+{q}_{y}j+{q}_{z}k$ are added the result is $\overrightarrow{p}+\overrightarrow{q}=({p}_{x}+{q}_{x})i$$+({p}_{y}+{q}_{y})j$$+({p}_{z}+{q}_{z})k$

When vectors in the component form are added, *the corresponding components are added.*

Outline

The outline of material to learn vector-algebra is as follows.

Note: Click here for detailed outline of vector-algebra.

• Introduction to Vectors

→ __Introducing Vectors__

→ __Representation of Vectors__

• Basic Properties of Vectors

→ __Magnitude of Vectors__

→ __Types of Vectors__

→ __Properties of Magnitude__

• Vectors & Coordinate Geometry

→ __Vectors & Coordinate Geometry__

→ __Position Vector of a point__

→ __Directional Cosine__

• Role of Direction in Vector Arithmetics

→ __Vector Arithmetics__

→ __Understanding Direction of Vectors__

• Vector Addition

→ __Vector Additin : First Principles__

→ __Vector Addition : Component Form__

→ __Triangular Law__

→ __Parallelogram Law__

• Multiplication of Vector by Scalar

→ __Scalar Multiplication__

→ __Standard Unit Vectors__

→ __Vector as Sum of Vectors__

→ __Vector Component Form__

• Vector Dot Product

→ __Introduction to Vector Multiplication __

→ __Cause-Effect-Relation__

→ __Dot Product : First Principles__

→ __ Dot Product : Projection Form__

→ __ Dot Product : Component Form__

→ __Dot Product With Direction__

• Vector Cross Product

→ __Vector Multiplication : Cross Product __

→ __Cross Product : First Principles__

→ __Cross Product : Area of Parallelogram__

→ __Cross Product : Component Form__

→ __Cross Product : Direction Removed__