maths > vector-algebra

Cross Product : Area of Parallelogram

    what you'll learn...


Vector Cross Product : Area of Parallelogram Form

 »  component in perpendicular is calculated by the angle
    →  p×q =|p||q|sinθn^
    →  Note that |b|=|q|sinθ
    →  |p||b| is the area of parallelogram with sides p and q


vector cross product area of the parallelogram

Vector cross product is understood as product between components in perpendicular. In the figure, The magnitude of p×q is 'the area of the parallelogram OLMN'.

Area of a parallelogram = base × height
The base is |p| and the height is |b|.

Two vectors p and q with magnitudes 2 and 3 respectively are at an angle 30. What is the area of the parallelogram made by p and q?

The answers are


Area of a Parallelogram made by two vectors: Given p and q, the area of the parallelogram made by them is
=|p×q| Vector cross product can be used to find area of the Parallelogram made by two vectors.


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