Question

If →A, →B, →C are mutually perpendicular, show that →C×(→A×→B)=0. Is the converse true?

Answer 1

sorry mate this ain't a part of my syllabus, in in 10th..

Answer 2

The converse is False.

Explanation:

Step 1:

It is shown that $A \rightarrow, B \rightarrow$ and $C \rightarrow$ are perpendicular mutually.

With the perpendicular direction to the plane, $A \rightarrow \times B \rightarrow$ is a vector containing .

$A \rightarrow \text { and } B \rightarrow$

There, the angle between $A \rightarrow \times B \rightarrow$ and $C \rightarrow$ is either $180^{\circ} \text { or } 0^{\circ}$.

Step 2:

That is, $C \rightarrow \times A \rightarrow \times B \rightarrow=0$

Yet, the converse is false. For instance, when both the vectors are parallel, then also, $C \rightarrow \times A \rightarrow \times B \rightarrow=$$0$

So, they should not be perpendicular mutually and the converse is false.