The vector equations of the two lines and are given by and

MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

The vector equations of the two lines

L_1

and

L_2

are given by

L_1 : \mathbf{r} = (2\mathbf{i} + 9\mathbf{j} + 13\mathbf{k}) + \lambda(\mathbf{i} + 2\mathbf{j} + 3\mathbf{k})

and

L_2 : \mathbf{r} = (-3\mathbf{i} + 7\mathbf{j} + p\mathbf{k}) + \mu(-\mathbf{i} + 2\mathbf{j} - 3\mathbf{k})

. Then, the lines

L_1

and

L_2

are (1) skew lines for all

p \in R

(2) intersecting for all

p \in R

and the point of intersection is

(-1, 3, 4)

(3) intersecting lines for

p = -2

(4) intersecting for all real

p \in R