"The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $-$ n = 0 and mn + nl + lm = 0, is :"

Question

Accepted Answer

"n = 2 (l + m)

lm + n(l + m) = 0

lm + 2(l + m)² = 0

2l² + 2m² + 5ml = 0

$2{\left( {{l \over m}} \right)^2} + 2 + 5\left( {{l \over m}} \right) = 0$

2t² + 5t + 2 = 0

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

$\Rightarrow t = - 2; - {1 \over 2}$

(i) ${l \over m} = - 2$

${n \over m} = - 2$

($-$2m, m, $-$2m)

($-$2, 1, $-$2)

(ii) ${l \over m} = - {1 \over 2}$

n = $-$2l

(l, $-$2l, $-$2l)

(1, $-$2, $-$2)

$$\cos \theta = {{ - 2 - 2 + 4} \over {\sqrt 9 \sqrt 9 }} = 0 \Rightarrow 0 = {\pi \over 2}$$"

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $-$ n = 0 and mn + nl + lm = 0, is :

Solution

About this question

Drill 25 more like these. Every day. Free.

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $-$ n = 0 and mn + nl + lm = 0, is :

Solution

About this question

More Three Dimensional Geometry questions

Drill 25 more like these. Every day. Free.