If |a| = √(26), |b| = 7 and |a x b| = 35, find vectors a.b.

Question

If |a| = \(\sqrt{26}\), |b| = 7 and |a x b| = 35, find vectors a.b.

Answer 1

Given \(|\vec a|=\sqrt{26},|\vec b| = 7\)  and  \(|\vec a\times\vec b|=35\)

We know the cross product of two vectors  \(\vec a\) and  \(\vec b\) forming an angle θ is

\(\vec a\times\vec b=|\vec a||\vec b|sin\,\theta\,\hat n\)

where \(\hat n\) is a unit vector perpendicular to \(\vec a\) and  \(\vec b\)

We also have the dot product of two vectors  \(\vec a\) and  \(\vec b\) forming and angle θ is