First slide

Direction ratios and direction cosines

Question

If the direction cosines of two lines are given by $l + m + n = 0 a n d \frac{1}{l} - \frac{2}{m} + \frac{1}{n} = 0$ , then the angle between them is

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{3}$
C

$\frac{π}{2}$
D

$0$

Solution

The standard concept:
$a = b = c = 1 and f = h = 1, g = - 2 \Rightarrow \frac{f}{a} + \frac{g}{b} + \frac{h}{c} = \frac{1}{1} - \frac{2}{1} + \frac{1}{1} = 0$
Therefore, both lines intersect at right angle.

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