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Thought-Process to Discover Knowledge

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mathsVector AlgebraVector Cross Product

Cross Product : Area of Parallelogram

In this page, you will learn about computing area of a parallelogram using vector cross product.



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Vector cross product is understood as product between components in perpendicular. vector cross product area of the parallelogram in the figure, What is the magnitude of `vec p xx vec q` ?

  • the area of the parallelogram OLMN
  • the area of the parallelogram OLMN
  • the perimeter of the parallelogram OLMN

The answer is 'the area of the parallelogram OLMN'.

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

Vector cross product can be used to find area of the Parallelogram made by two vectors.

Area of a Parallelogram made by two vectors: Given `vec p` and `vec q`, the area of the parallelogram made by them is
`= |vec p xx vec q|`

Solved Exercise Problem:

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

  • `2 xx 3 xx sin 30^@`
  • `2 xx 3 xx 1/2`
  • `3`
  • all the above
  • all the above

The answer is 'All the above'

                            
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