Download App

STD 12 - 11. three dimension geometry — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 11. three dimension geometry4 Marks
Question
If two straight lines whose direction cosines are given by the relations $l+m-n=0,3l^{2}+m^{2}+c n l =0$ are parallel, then the positive value of $c$ is
✓

Answer

a
$1+ m - n =0$

$3 l^{2}+ m ^{2}+ cl (1+ m )=0$

$n =1+ m$

$3 l ^{2}+ m ^{2}+ cl ^{2}+ clm =0$

$(3+ c ) l ^{2}+ clm + m ^{2}=0$

$(3+c)\left(\frac{l}{m}\right)^{2}+c\left(\frac{l}{m}\right)+1=0 \ldots \ldots(1)$

$\because$ lies are parallel.

Roots of $(1)$ must be equal

$\Rightarrow D=0$

$c ^{2}-4(3+ c )=0$

$c ^{2}-4 c -12=0$

$( c -6)( c +2)=0$

$c =6$ or $c =-2$

$+ve$ value of $c =6$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The number of permutations of the letters $a_1, a_2, a_3, a_4, a_5$ in which the first letter $a_1$ does not occupy the first position (from the left) and the second letter $a_2$ does not occupy the second position (from the left) is
→
Consider the set $A_n$ of points $(x, y)$ such that $0 \leq x \leq n, 0 y \leq n$ where $n, x, y$ are integers. Let $S_n$ be the set of all lines passing through at least two distinct points from $A_n$. Suppose we choose a line $l$ at random from $S_n$. Let $P_n$ be the probability that $l$ is tangent to the circle $x^2+y^2=n^2\left(1+\left(1-\frac{1}{\sqrt{n}}\right)^2\right)$ Then, the limit $\lim _{n \rightarrow \infty} P_n$ is
→
Let $y(x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\left(1+x^{16}\right)$

Then $y^{\prime}-y^{\prime \prime}$ at $x=-1$ is equal to

→
For a point $P$ in the plane, let $d_1(P)$ and $d_2(P)$ be the distance of the point $P$ from the lines $x-y=0$ and $x+y=0$ respectively. The area of the region $R$ consisting of all points $P$ lying in the first quadrant of the plane and satisfying $2 \leq d_1(P)+d_2(P) \leq 4$, is
→
Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$. Then, the number of ways of choosing $x$ and $y$, such that $x + y$ is divisible by $5$ , is $.........$.
→
The sum of the series
$2 \times 1 \times{ }^{20} \mathrm{C}_{4}-3 \times 2 \times{ }^{20} \mathrm{C}_{5}+4 \times 3 \times{ }^{20} \mathrm{C}_{6}-5 \times 4 \times$ ${ }^{20} \mathrm{C}_{7}+\ldots+18 \times 17 \times{ }^{20} \mathrm{C}_{20}$, is equal to __________ .
→
Let a curve $y = y ( x )$ pass through the point $(3,3)$ and the area of the region under this curve, above the $x$-axis and between the abscissae $3$ and $x(>3)$ be $\left(\frac{y}{x}\right)^{3}$. If this curve also passes through the point $(\alpha, 6 \sqrt{10})$ in the first quadrant, then $\alpha$ is equal to $........$
→
$\left| {\,\begin{array}{*{20}{c}}{11}&{12}&{13}\\{12}&{13}&{14}\\{13}&{14}&{15}\end{array}\,} \right| = $
→
The number of integers $x$ satisfying $-3 x^4+\operatorname{det}\left[\begin{array}{ccc}1 & x & x^2 \\ 1 & x^2 & x^4 \\ 1 & x^3 & x^6\end{array}\right]=0$ is equal to
→
If $[t]$ denotes the greatest integer $\leq t$, then number of points, at which the function $f ( x )=4|2 x +3|+$ $9\left[x+\frac{1}{2}\right]-12[x+20]$ is not differentiable in the open interval $(-20,20)$, is$.....$
→