If \(\vec{a} . \vec{c} =3 , \vec{a} = \hat{i}+ \hat{j}+ \hat{k}, \vec{b} =\hat{j} – \hat{k}, \vec{a} \times \vec{c} =\vec{b}\), Find \([\vec{a} \ \; \vec{b} \;\; \vec{c}]\)
Answer
\([\vec{a} \ \; \vec{b} \;\; \vec{c}]\) = -2
Solution:
Given \(\vec{a} . \vec{c} =3 , \vec{a} = \hat{i}+ \hat{j}+ \hat{k}, \vec{b} =\hat{j} – \hat{k}, \vec{a} \times \vec{c} =\vec{b}\)
This implies, \((\vec{a} \times \vec{c})⋅.\vec{b} =\vec{b}.\vec{b}\)
or \([\vec{a} \ \; \vec{b} \;\; \vec{c}]\) = -2