The plane XOZ divides the join of (1, , - 1, , ,5) and (2, 3, 4) … - Vidyadip

MCQ

The plane $XOZ$ divides the join of $(1,\, - 1,\,\,5)$ and $(2, 3, 4)$ in the ratio $\lambda :1$, then $\lambda $ is

A
$-3$
B
$3$
C
$ - \frac{1}{3}$
✓
$\frac{1}{3}$

✓

Answer

Correct option: D.

$\frac{1}{3}$

d
(d) Since $ZOX$ plane i.e. $y = 0$ divides the join of $(1,-1, 5)$ and $(2, 3, 4)$ in the ratio $\lambda \,\,:1$.

$\therefore \,\,\,\frac{{3\lambda - 1}}{{\lambda + 1}} = 0\,\, $

$\Rightarrow \,\,\lambda = \frac{1}{3}$.

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

More "M.C.Q (1 Marks)" from STD 12 - 11. three dimension geometry→STD 12 - 11. three dimension geometry — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Consider the function $f (x) = x^3 - 8x^2 + 20x -13$
Number of positive integers $x$ for which $f (x)$ is a prime number, is

$\text{f}(\text{x})=\sin +\sqrt{3}\cos\text{x}$ is maximum when x =

$\lim _{n \rightarrow \infty}\left(\frac{n^{2}}{\left(n^{2}+1\right)(n+1)}+\frac{n^{2}}{\left(n^{2}+4\right)(n+2)}+\frac{n^{2}}{\left(n^{2}+9\right)(n+3)}+\ldots+\frac{n^{2}}{\left(n^{2}+n^{2}\right)(n+n)}\right)$ is equal to

If the system of equations

$x+y+z=2$

$2 x+4 y-z=6$

$3 x+2 y+\lambda z=\mu$ has infinitely many solutions, then

The probability that in a year of $22^{nd}$ century chosen at random, there will be $53$ Sunday, is

The number of values of $k $ for which the system of equations $(k + 1)x + 8y = 4k,$ $kx + (k + 3)y = 3k - 1$ has infinitely many solutions, is

The area enclosed between the curves ${y^2} = x$ and $y = \left| x \right|$ is

If $f\left( x \right) = {x^3} + {e^{\frac{x}{2}}}$ and $g\left( x \right) = {f^{ - 1}}\left( x \right)$ then value of $g '(1)$ is

If $\sin y = x\cos (a + y),$ then ${{dy} \over {dx}} = $

Let $f, g$ and $h$ be real-valued functions defined on the interval $[0,1]$ by $f(x)=e^{x^2}+e^{-x^2}, g(x)$ $=x e^{x^2}+e^{-x^2}$ and $h(x)=x^2 e^{x^2}+e^{-x^2}$. If $a, b$ and $c$ denote, respectively, the absolute maximum of $f, g$ and $\mathrm{h}$ on $[0,1]$, then