Question

If two straight lines whose direction cosines are given by the relations l + m – n = 0, 3l² + m² + cnl = 0 are parallel, then the positive value of c is ______.

Options

• 6

• 4

• 3

• 2

Answer 1

If two straight lines whose direction cosines are given by the relations l + m – n = 0, 3l² + m² + cnl = 0 are parallel, then the positive value of c is 6.

Explanation:

Given equations are

l + m – n = 0 `\implies` n = l + m

Now, put the value of n in another equation then,

3l² + m² + cl (l + m) = 0

3l² + m² + cl² + clm = 0

(3 + c)l² + clm + m² = 0

`(3 + c)(l/m)^2 + c(l/m) + 1` = 0  ...(i)

Given that lines are parallel.

Then, roots of (i) must be equal `\implies` D = 0

c² – 4(3 + c) = 0 `\implies` c³ – 4c – 12 = 0

(c – 6) (c + 2) = 0 `\implies` c = 6 or c = –2.

Therefore, +ve value of c = 6.