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 the points $(-1, 3, 2), (-4, 2, -2)$ and $(5,\,\,5,\,\,\lambda )$ are collinear, then $\lambda $=
✓

Answer

d
(d) $\frac{{ - 4 + 1}}{{5 + 4}} = \frac{{2 - 3}}{{5 - 2}} = \frac{{ - 2 - 2}}{{\lambda + 2}}$ or $\lambda + 2 = 12$ or $\lambda = 10$.

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

Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to.....................
→
The number of points at which the function $f(x) = |x - 0.5| + |x - 1| + \tan x$ does not have a derivative in the interval $(0, 2),$ is
→
Let $C_1$ and $C_2$ be the centres of the circles $x^2 + y^2 -2x -2y -2 = 0$ and $x^2 + y^2 - 6x-6y + 14 = 0$ respectively. If $P$ and $Q$ are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral $PC_1QC_2$ is ............. $\mathrm{sq. \, units}$
→
The area of the region $\left\{(x, y): x^2 \leq y \leq 8-x^2, y \leq 7\right\}$ is
→
If the solution curve $y = yx$ of the differential equation $\left(1+y^2\right)\left(1+\log _e x\right) d x+x\  d y=0, x>0$ passes through the point $(1,1)$ and $y(c)=\frac{\alpha-\tan \left(\frac{3}{2}\right)}{\beta+\tan \left(\frac{3}{2}\right)},$ then $\alpha+2 \beta$ is
→
If the shortest distance between the lines

$ \mathrm{L}_1: \overrightarrow{\mathrm{r}}=(2+\lambda) \hat{\mathrm{i}}+(1-3 \lambda) \hat{\mathrm{j}}+(3+4 \lambda) \hat{\mathrm{k}}, \lambda \in \mathbb{R} $

$ \mathrm{L}_2: \overrightarrow{\mathrm{r}}=2(1+\mu) \hat{\mathrm{i}}+3(1+\mu) \hat{\mathrm{j}}+(5+\mu) \hat{k}, \mu \in \mathbb{R}$

is $\frac{\mathrm{m}}{\sqrt{\mathrm{n}}}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then the value of $\mathrm{m}+\mathrm{n}$ equals.

→
Let a ray of light passing through the point $(3,10)$ reflects on the line $2 x+y=6$ and the reflected ray passes through the point $(7,2)$. If the equation of the incident ray is $a x+$ by $+1=0$, then $a^2+b^2+3 a b$ is equal to..................
→
Let $A$ be the area of the region $\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$ Then $540\,A$ is equal to
→
Let $f\left( x \right) = x\sqrt {x\sqrt {x\sqrt {x.......\infty } } } \left( {x > 0} \right)$ ,then $f'(3)$ is equal to 
→
If the integral $\int_{0}^{10} \frac{[\sin 2 \pi x ]}{ e ^{ x -[ x ]}} dx =\alpha e ^{-1}+\beta e ^{-\frac{1}{2}}+\gamma$, where $\alpha, \beta, \gamma$ are integers and $[ x ]$ denotes the greatest integer less than or equal to $x$, then the value of $\alpha+\beta+\gamma$ is equal to ........ .
→