TS EAMCET 5 May 2018 Shift 1 Solved Paper

The direction cosines of two lines satisfy the equations,
l+m+n=0
m=−(l+n) …… (1)
And,
2lm+2‌ln−mn=0…… (2)
The above expression is expressed as,
2ln+m(2l−n)=0
From equation (1),
2ln−(l+n)(2l−n)=0
(l−n)(2l+n)=0
l=n and l=−

n

2

…… (3)
Substitute the value in equation (1), then

m

−2

=n and m=−

n

2

…… (4)
From equation ( 3 ) and (4),

l

1

=

m

−2

=

n

1

and

l

1

=

m

1

=

n

−2

The acute angle between lines is,
cos‌θ =|

1×1+(−2)×1+1×(−2)

√12+22+12√12+12+22

|
cos‌θ=

1

2

θ=60°