Question

The direction cosines of a line which is perpendicular to both the lines whose direction ratios are -2, 1, -1 and -3, -4, 1 are ______ 

विकल्प

• `(-3)/sqrt155, 5/sqrt155, 11/sqrt155`

• `(3)/sqrt155, (-5)/sqrt155, 11/sqrt155`

• `(3)/sqrt155, 5/sqrt155, (-11)/sqrt155`

• `(3)/sqrt155, 5/sqrt155, 11/sqrt155`

Answer 1

The direction cosines of a line which is perpendicular to both the lines whose direction ratios are -2, 1, -1 and -3, -4, 1 are `underline((-3)/sqrt155, 5/sqrt155, 11/sqrt155)`.

Explanation:

Let the direction ratio of the line perpendicular to both the lines be a, b, c.

The line is perpendicular to the lines with direction ratios -2, 1, -1 and -3, -4, 1

∴ -2a + b - c = 0 ....... (i)

-3a - 4b + c = 0 · .... (ii)

Solving (i) and (ii), we get

`a/(-3) = b/5 = c/11`

∴ The d.r.s. of the line are -3, 5, 11.

∴ The required d.c.s. of the line are `(-3)/sqrt155, 5/sqrt155, 11/sqrt155`.