L_2: r = pmatrix 6 -7 4 pmatrix + pmatrix -4 10 -6 pmatrix

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

Problem

l_1: \mathbf{r} = \begin{pmatrix} 0 \\ 8 \\ -5 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ -5 \\ 3 \end{pmatrix}

l_2: \mathbf{r} = \begin{pmatrix} 6 \\ -7 \\ 4 \end{pmatrix} + \mu \begin{pmatrix} -4 \\ 10 \\ -6 \end{pmatrix}.

Show that the lines

l_1

and

l_2

have the same direction and determine whether they are coincident or parallel.