Question

If the direction ratios of two non parallel lines are connected by the relation 3a+b+5c and 5ab+6bc-2ca , then the angle between the lines is​

Answer 1

Answer:

Correct option is

D

2

π

Given 3lm−4ln+mn=0 ...(1)

and l+2m+3n=0 ....(2)

From equation (2), l=−(2m+3n), putting in equation (1), we get

−3(2m+3n)m+4(2m+3n)n+mn=0

⇒−6m

2

+12n

2

=0⇒m=±

2

n

Now, m=±

2

n⇒l=−(2

2

n+3n)=−(2

2

+3)n

∴l:m:n=−(3+2

2

)n:

2

n:n=−(3+2

2

):−

2

:1

Also, m=−

2

n⇒l=−(−2

2

+3)n

∴l:m:n=−(3−2

2

)n:−

2

n:n=−(3−2

2

):−

2

:1

⇒cosθ=

(3+2

2

)

2

+(

2

)

2

+1

2

(3−2

2

)

2

+(−

2

)

2

+1

2

(3+2

2

)(3−2

2

)+(

2

)(−

2

)+1.1

⇒θ=

2

π