First slide

Direction ratios and direction cosines

Question

The acute angle between the two lines whose d.r’s are given by the equations $l + m + n = 0$ and $l^{2} + m^{2} - n^{2} = 0$ is

Moderate

A

0
B

$\frac{π}{6}$
C

$\frac{π}{4}$
D

$\frac{π}{3}$

Solution

Given n=-l-m
$l^{2} + m^{2} - {(- l - m)}^{2} = 0 2 l m = 0 l = 0 o r m = 0 l = 0 \Rightarrow n = - m (l, m, n) = (0, 1, - 1) s i m i l a r l y m = 0$
(0,1,-1)and(1,0,-1)
Solve the given two equation for the d.r's of the lines and use $\cos θ$ formula

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