Area of Parallelogram in Vector form
Area of Parallelogram in vector form involves using vectors to express the sides of the parallelogram and then calculating the cross-product of those vectors. The cross-product yields a vector that represents the area of the parallelogram.
Area of Parallelogram can be calculated even when the sides and the diagonals of the parallelogram are given in vector form. Considering a parallelogram PQRS, with adjacent sides and respectively. And the diagonals are and .
Now, Area of Parallelogram in vector form is given using adjacent sides and as,
UsingParallelogram Law of Vector Addition
Now,
But, , and
Therefore,
Thus from equation (1), the area of the parallelogram in vector form is stated as:
Example: Find the area of a parallelogram whose adjacent sides are vectors. A = 2i + 5j and B = 7i – j
Area of Parallelogram = |A × B|
A =
A = i(0-0) – j(0-0) + k(-2-35) = -35k
Area of Prarallelogram is -35k units
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Area of Parallelogram | Definition, Formulas & Examples
The area of a Parallelogram is the space or the region enclosed by the boundary of the parallelogram in a two-dimensional space. It is calculated by multiplying the base of the parallelogram by its height. In this article, we will learn more about the Area of Parallelogram Formulas, and how to use them with the help of examples.
Table of Content
- What is the Area of Parallelogram?
- Formulas – Area of a Parallelogram
- Area of Parallelogram Formula
- How to Find Area of Parallelogram?
- Area of Parallelogram using Base and Height
- Area of Parallelogram using Side Lengths
- Area of Parallelogram using Diagonals
- Area of Parallelogram in Vector form
- Area of Parallelogram Solved Examples
- Practice Questions on Area of Parallelogram