The distance between the line [ r = 2 i - 2 j + 3 k + ( i - j + 4k ),] and the plane [ r .…

Question

The distance between the line

$$\overrightarrow r  = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),$$ and the plane

$$\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5$$ is

Accepted Answer

A point on lines is $$\left( {2, - 2,3} \right)$$ its perpendicular distance

from the plane $x + 5y + z - 5 = 0$ is

$$ = \left| {{{2 - 10 + 3 - 5} \over {\sqrt {1 + 25 + 1} }}} \right| = {{10} \over {3\sqrt 3 }}$$

Solutions · 1