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

MCQ

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

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

✓

Answer

Correct option: D.

$\frac{1}{3}$

The plane $\text{XOZ}$ divides the join of $(1, -1, 5)$ and $(2, 3, 4)$ in the ratio $\lambda:1$
i.e. $y = 0$ divide 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 Introduction to Three Dimensional Geometry→Introduction to Three Dimensional Geometry — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $A$ and $B$ are two fixed points and $P$ is a variable point such that $PA + PB = 4$, then the locus of $P$ is a/an

The figure formed by the lines $\text{ax} \pm \text{by} \pm \text{c} = 0 $ is:

If the complex numbers ${z_1},{z_2},{z_3}$ represent the vertices of an equilateral triangle such that $|{z_1}| = |{z_2}| = |{z_3}|,$ then ${z_1} + {z_2} + {z_3}$=

If $(1-\text{x}^{2})^{\text{n}}=\sum_{\text{r}=0}^{\text{n}}\text{a}_{\text{r}}\text{x}^{\text{r}}(1-\text{x})^{2\text{n}-\text{r}},$ then $a_r$ is equal to:

Let $\mathrm{P}(\alpha, \beta)$ be a point on the parabola $\mathrm{y}^2=4 \mathrm{x}$. If $\mathrm{P}$ also lies on the chord of the parabola $x^2=8 y$ whose mid point is $\left(1, \frac{5}{4}\right)$. Then $(\alpha-28)(\beta-8)$ is equal to...................

Let $z$ be a complex number satisfying $|z - 5i|\, \le 1$ such that amp $z$ is minimum. Then $z$ is equal to

If the chord $y = mx + 1$ of the circle ${x^2} + {y^2} = 1$ subtends an angle of measure ${45^o}$ at the major segment of the circle then value of $m$ is

The vertex of the parabola $y^2- 4y - x + 3 = 0$ is:

A bag contains $5$ distinct Red, $4$ distinct Green and $3$ distinct Black balls. Balls are drawn one by one without replacement,then the probability of getting a particular red ball in fourth draw is-

If $\mathrm{n}$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $\mathrm{n}$ is equal to: