​ If vector a + vector b + vector c = 0 , show that vector b x vector c = vector c x vector a . Interpret the result geometrically? ​

Question

If \(\vec a + \vec b + \vec c = 0\), show that \(\vec a \times \vec b = \vec b \times \vec c = \vec c \times \vec a\) . Interpret the result geometrically?

Answer 1

Now, let us interpret the result graphically.

Let there be a parallelogram ABCD.

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,

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