If `|vec(a)| = sqrt(26) , |vec(b)| = 7` , and `| vec(a) xx vec(b)| = 35`. Find `vec(a) . Vec(b)`.

Explanation

To find the dot product \( \vec{a} \cdot \vec{b} \) given the magnitudes of the vectors and the magnitude of their cross product, we can use the following relationships:

1. The magnitude of the cross product is given by:
\[ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin \theta \]
where \( \theta \) is the angle between the two vectors.

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