Question

If \[\vec{a}\] lies in the plane of vectors \[\vec{b} \text { and } \vec{c}\], then which of the following is correct?

Options

• \[\left[ \vec{a} \vec{b} \vec{c} \right] = 0\]

• \[\left[ \vec{a} \vec{b} \vec{c} \right] = 1\]

• \[\left[ \vec{a} \vec{b} \vec{c} \right] = 3\]

• \[\left[ \vec{b} \vec{c} \vec{a} \right] = 1\]

Answer 1

\[\left[ \vec{a} \vec{b} \vec{c} \right] = 0\]

\[\text { If } \vec{ a} \text { lies in the plane of vectors }\vec{b} and \vec{c} , then \vec{a} , \vec{b} , \vec{c} \text { will lie in the same plane, i . e . they will be coplanar} . \]

\[ \therefore \left[ \vec{a} \vec{b} \vec{c} \right] = 0\]