Statement I If the vectors and are non-collinear then the lines and are coplanar

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Statement I If the vectors

\mathbf{a}

and

\mathbf{c}

are non-collinear then the lines

\mathbf{r} = 6\mathbf{a} - \mathbf{c} + \lambda(2\mathbf{c} - \mathbf{a})

and

\mathbf{r} = \mathbf{a} - \mathbf{c} + \mu(\mathbf{a} + 3\mathbf{c})

are coplanar. Statement II There exist

\lambda

and

\mu

such that the two values of

\mathbf{r}

in Statement I becomes same.