First slide

Direction ratios and direction cosines

Question

If the direction cosines between two lines are given by the relations $a l + b m + c n = 0$ and $h l m + f m n + g n l = 0$ , then the two lines are parallel. if $\sqrt{a f} \pm \sqrt{b g} \pm \sqrt{c h} + \sqrt{(- 4)} =$

Moderate

A

0
B

$- 3 i$
C

2
D

$2 i$

Solution

If the direction cosines between two lines are related by the relations $a l + b m + c n = 0$ and $h l m + f m n + g n l = 0$ , then the condition that the lines are to be parallel is $\sqrt{a f} \pm \sqrt{b g} \pm \sqrt{c h} = 0$
It implies that $\sqrt{a f} \pm \sqrt{b g} \pm \sqrt{c h} + \sqrt{(- 4)} = 0 + 2 i = 2 i$

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