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Dot product with Added Direction

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Dot Product with Added Direction

 »  By definition, dot product is scalar

 »  Some applications may specify an additional direction in the multiplication of components in parallel. In such cases, the direction is combined.

think different

An object by position vector p casts a shadow on a screen. The screen in given by unit vector s. The shadow is a vector that spans as a ray with a starting and end point.

vector dot product shadow example

p and the screen s^ are given. The length of the shadow is ps^ which is a scalar |p|cosθ

The shadow is a vector along the direction of s^ and the length of the shadow is ps^. Combining thest to the shadow is given as (ps^)s^


Projection vector using Dot Product: For a vector p and a direction given by unit vector s^, the projection vector of p in direction s^ is (ps^)s^.

Vector dot product by definition is a scalar. Depending on the application requirement, a direction can be added to the scalar.


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