Given three vectors

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Given three vectors

\mathbf{U} = 2\hat{\mathbf{i}} + 3\hat{\mathbf{j}} - 6\hat{\mathbf{k}}

\mathbf{V} = 6\hat{\mathbf{i}} + 2\hat{\mathbf{j}} + 3\hat{\mathbf{k}}

and

\mathbf{W} = 3\hat{\mathbf{i}} - 6\hat{\mathbf{j}} - 2\hat{\mathbf{k}}

which of the following hold good for the vectors

\mathbf{U}

\mathbf{V}

and

\mathbf{W}

? (1)

\mathbf{U}

\mathbf{V}

and

\mathbf{W}

are linearly dependent (2)

(\mathbf{U} \times \mathbf{V}) \times \mathbf{W} = 0

(3)

\mathbf{U}

\mathbf{V}

and

\mathbf{W}

form a triplet of mutually perpendicular vectors (4)

(\mathbf{U} \times \mathbf{V} \times \mathbf{W}) = 0