Consider the lines and

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · ISC

Problem

Consider the lines

L_1 : \mathbf{r} = \mathbf{a} + \lambda \mathbf{b}

and

L_2 : \mathbf{r} = \mathbf{b} + \mu \mathbf{a}

, where

\mathbf{a}

and

\mathbf{b}

are non-zero and non-collinear vectors. Statement I

L_1

and

L_2

are coplanar and the plane containing these lines passes through origin. Statement II

(\mathbf{a} - \mathbf{b}) \cdot (\mathbf{b} \times \mathbf{a}) = 0

and the plane containing

L_1

and

L_2

[\mathbf{r} \mathbf{a} \mathbf{b}] = 0

which passes through origin.