A line passing through a point with position vector and parallel

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

Problem

A line

L_1

passing through a point with position vector

\mathbf{p} = \hat{i} + 2\hat{j} + 3\hat{k}

and parallel

\mathbf{a} = \hat{i} + 2\hat{j} + 3\hat{k}

. Another line

L_2

passing through a point with position vector

= 2\hat{i} + 3\hat{j} + 3\hat{k}

and parallel to

\mathbf{b} = 3\hat{i} + \hat{j} + 2\hat{k}

. Equation of plane equidistant from line

L_1

and

L_2

is (1)

\hat{r} \cdot (\hat{i} - 7\hat{j} - 5\hat{k}) = 3

(2)

\hat{r} \cdot (\hat{i} + 7\hat{j} + 5\hat{k}) = 3

(3)

\hat{r} \cdot (\hat{i} - 7\hat{j} - 5\hat{k}) = 9

(4)

\hat{r} \cdot (\hat{i} + 7\hat{j} - 5\hat{k}) = 9