Question

If two straight lines whose direction cosines are given by the relations $l + m – n = 0$, $3l^2 + m^2 + cnl = 0$ are parallel, then the positive value of $c$ is :

• A. 6
• B. 4
• C. 3
• D. 2

Answer 1

Answer: (A)

6

Answer 2

$l + m – n = 0$
$⇒n = l + m$
$3l^2 + m^2 + cnl = 0$
$3l^2 + m^2 + cl(l + m) = 0$
$⇒ (3 + c)l^2 + clm + m^2 = 0$
$⇒(3+c)(\frac Im)^2+c(\frac Im)+1=0$
∵ The lines observed are parallel to each other
Therefore, $D = 0$
$⇒ c^2 – 4(3 + c) = 0$
$⇒ c^2 – 4c – 12 = 0$
$(c – 6)(c \+ 2) = 0$
$⇒c = 6$ (because $c>0$)

So, the correct option is (A): $6$