Mathematics

Mathematics

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 a. skew lines for all

p \in R

b. intersecting for all

p \in R

and the point of intersection is

(-1, 3, 4)

c. intersecting lines for

p = -2

d. intersecting for all real

p \in R

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