Show that the line passing through the points (4, 7, 8) (2, 3, 4)… - Vidyadip

Question

Show that the line passing through the points (4, 7, 8) (2, 3, 4) is parallel to the passing through the points (-1, -2, 1), (1, 2, 5)

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Answer

Direction Ratios (D.R.s) of Line 1 $\left(L_1\right): a_1=x_2-x_1$
$=2-4$
$=-2$
$\therefore$ $b_1=y_2-y_1$
= $3-7$
$=-4$
$\therefore$ $c_1=z_2-z_1$
$=4-8$
$=-4$
$\therefore$ D.R.s of $L_1:(-2,-4,-4)$
Direction Ratios (D.R.s) of Line 2 $\left(L_2\right): a_2=1-(-1)$
$=2 b_2$
$\therefore$ $b_2=2-(-2)$
$=4 c_2$
= $5-1$
$=4$
$\therefore$ D.R.s of $L_2:(2,4,4)$
Check for Parallelism: Lines are parallel if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{-2}{2}=-1 ;$
$\frac{-4}{4}=$ -1;
$\therefore$ $\frac{-4}{4}=-1$ Since the ratios are equal, the lines are parallel.

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