Triangular Law

Overview

**Vector Addition : Triangular Law**

» **sequential addition** of $\overrightarrow{p}$ and $\overrightarrow{q}$

→ the third side of the triangle formed by $\overrightarrow{p}$ and $\overrightarrow{q}$

sequential

In a bucket there is $20$ liter water and another $10$ liter water is poured in. The bucket has $20+10=30$ liter of water.

With $20$ liter, another $10$ liter is added. * Scalar quantities can be added sequentially.*

Two taps simultaneously fill a bucket. One fills at $20$ liter per hour and another fills at $10$ liter per hour. At the end of an hour, the bucket has $20+10=30$ liter of water.

Two streams of water are added into the bucket. *Scalar quantities can be added continuously*.

We have seen that two ways scalar quantities can be added - Sequentially and Continuously.

How about vectors?

A person walks for $1$ units at $24}^{\circ$ , then from that point, walks for $2.3$ units at $43}^{\circ$ angle. Addition of these two vectors is an example of Sequential addition of vectors. At the end of the first vector, the second vector starts and added.

Two vectors are added sequentially as given in the figure. The result of the addition is 'the third side of the triangle'.

Two vectors form a triangle with the sum as the *third side of the triangle*.

summary

**Triangular Property of vector addition: ** : When two vectors are added, arrange the initial point of the second vector to the terminal point of the first vector. In that position, complete the triangle with the two vectors as the two sides. The third side, connecting initial point of the first vector and the terminal point of the second vector, is the sum of the two vectors.

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__