If `veca , vecb and vecc ` are three vectors such that `vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb` then prove that `|veca|= |vecb|=|vecc|`

Explanation

To prove that \(|\vec{a}| = |\vec{b}| = |\vec{c}|\) given the conditions \(\vec{a} \times \vec{b} = \vec{c}\), \(\vec{b} \times \vec{c} = \vec{a}\), and \(\vec{c} \times \vec{a} = \vec{b}\), we can follow these steps:

### Step 1: Dot Product of \(\vec{c}\) with \(\vec{c}\)
We start with the first equation:
\[ \vec{a} \times \vec{b} = \vec{c} \]
Now, take the dot product of both sides with \(\vec{c}\):
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