If two straight lines whose direction cosines | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the relations for direction cosines $l, m, n$ are $l+m-n=0$ and $3l^{2}+m^{2}+cnl=0$. From the first equation,we have $n = l+m$. Substitutin

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(A) Given the relations for direction cosines $l, m, n$ are $l+m-n=0$ and $3l^{2}+m^{2}+cnl=0$. From the first equation,we have $n = l+m$. Substituting this into the second equation: $3l^{2}+m^{2}+cl(l+m)=0$. Expanding this,we get $3l^{2}+m^{2}+cl^{2}+clm=0$. Grouping the terms,we have $(3+c)l^{2}+clm+m^{2}=0$. Dividing by $m^{2}$ (assuming $m 
eq 0$),we get $(3+c)(\frac{l}{m})^{2}+c(\frac{l}{m})+1=0$. Since the two lines are parallel,the roots of this quadratic equation in $(\frac{l}{m})$ must be equal. Therefore,the discriminant $D = b^{2}-4ac = 0$. $c^{2}-4(3+c)(1) = 0$. $c^{2}-4c-12=0$. Factoring the quadratic,we get $(c-6)(c+2)=0$. This gives $c=6$ or $c=-2$. Since we need the positive value of $c$,we have $c=6$.

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

Similar Questions

The direction cosines of a line which lies in the $ZOX$ plane and makes an angle of $30^{\circ}$ with the $Z$-axis are

If a line has the direction ratios $-18, 12, -4,$ then what are its direction cosines?

The direction cosines of the line $\frac{x-1}{0}=\frac{y+1}{5}=\frac{z-3}{0}$ are . . . . . . .

The direction cosines of a line segment $AB$ are $-2/\sqrt{17}, 3/\sqrt{17}, -2/\sqrt{17}$. If $AB = \sqrt{17}$ and the coordinates of $A$ are $(3, -6, 10)$,then the coordinates of $B$ are

The projection of the line segment joining the points $(-1, 0, 3)$ and $(2, 5, 1)$ on the line whose direction ratios are $6, 2, 3$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module