QJEEM21Ma65a6: JEE Main 2021 Mathematics - Class 12 JEEM21Ma65a6 Solution: The angle between the straight lines, whose direction cosines…

Question

Verified Solution • 2025–26 Session moderate

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m

-

n = 0 and mn + nl + lm = 0, is :

Accepted Answer

n = 2 (l + m)

lm + n(l + m) = 0

lm + 2(l + m)² = 0

2l² + 2m² + 5ml = 0

2 {(\frac{l}{m})}^{2} + 2 + 5 (\frac{l}{m}) = 0

2t² + 5t + 2 = 0

(t + 2)(2t + 1) = 0

\Rightarrow t = - 2; - \frac{1}{2}

(i)

\frac{l}{m} = - 2

\frac{n}{m} = - 2

(

-

2m, m,

-

2m)

(

-

2, 1,

-

2)

(ii)

\frac{l}{m} = - \frac{1}{2}

n =

-

2l

(l,

-

2l,

-

2l)

(1,

-

2,

-

2)

\cos θ = \frac{- 2 - 2 + 4}{\sqrt{9} \sqrt{9}} = 0 \Rightarrow 0 = \frac{π}{2}

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