Find `| vec a|`and `| vec b|`, if `( vec a+ vec b)dot(( vec a- vec b))=8`and `|vec a|=8 | vec b|`

Explanation

To solve the problem, we need to find the magnitudes of vectors \(\vec{a}\) and \(\vec{b}\) given the conditions:

1. \((\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 8\)
2. \(|\vec{a}| = 8 |\vec{b}|\)

Let's denote \(|\vec{b}| = b\). Then, from the second condition, we have:

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