If , show that . Interpret the result geometrically?

Given that,

Find the value of .

Take .

[∵ ]

…(i)

[∵ by anti-commutative law, ]

Now, take .

[∵ ]

…(ii)

[∵ by anti-commutative law, ]

From equations (i) and (ii), we have

Now, let us interpret the result graphically.

Let there be a parallelogram ABCD.

Here, and .

And AB and AD sides are making angle θ between them.

Area of parallelogram is given by,

Area of parallelogram = Base × Height

So from the diagram, area of parallelogram ABCD can be written as,

Or,

Since, parallelogram on the same base and between the same parallels are equal in area, so we have

This also implies that,

Thus, it is represented graphically.