JEE Main · 2014 · 06 Apr 2014 · Offline · Three Dimensional Geometry

The angle between the lines whose direction cosines satisfy the equations

l + m + n = 0

and

l^{2} = m^{2} + n^{2}

(A) $\frac{π}{3}$ ✓ Correct
(B) $\frac{π}{4}$
(C) $\frac{π}{6}$
(D) $\frac{π}{2}$

Answer: (A)

Solution

From

l + m + n = 0

take

l = - (m + n)

and put it into

l^{2} = m^{2} + n^{2}

(m + n)^{2} = m^{2} + n^{2}

gives

2 mn = 0

, so either

m = 0

n = 0

. If

m = 0

then

l = - n

and, after normalising, the direction cosines are

(- \frac{1}{2}, 0, \frac{1}{2})

; if

n = 0

they are

(- \frac{1}{2}, \frac{1}{2}, 0)

. The angle between these two directions has

cos θ = \frac{1}{2} = \frac{1}{2}

, so

θ = \frac{π}{3}

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option

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