MHT CET 2021 22th September Morning Shift | Three Dimensional Geometry Question 84 | Mathematics

The plane $$\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1$$ cuts the $$X$$-axis at A, Y-axis at B and Z-axis at C, then the area of $$\triangle \mathrm{ABC}=$$

$$\sqrt{71}$$ sq. units

$$\sqrt{29}$$ sq. units

$$\sqrt{41}$$ sq. units

$$\sqrt{61}$$ sq. units

MHT CET 2021 22th September Morning Shift

MCQ (Single Correct Answer)

-0

If a plane meets the axes $$\mathrm{X}, \mathrm{Y}, \mathrm{Z}$$ in $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ respectively such that centroid of $$\triangle \mathrm{ABC}$$ is $$(1,2,3)$$, then the equation of the plane is

$$x+2 y+3 z=1$$

$$x+\frac{y}{2}+\frac{z}{3}=3$$

$$\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1$$

$$\frac{x}{4}+\frac{y}{8}+\frac{z}{12}=1$$

MHT CET 2021 22th September Morning Shift

MCQ (Single Correct Answer)

-0

The shortest distance between lines $$\bar{r}=(2 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})$$ and $$\bar{r}=(\hat{r}-\hat{j}+2 \hat{k})+\mu(2 \hat{i}+\hat{j}-5 \hat{k})$$ is

$$\frac{1}{\sqrt{5}}$$

3 units

$$\sqrt{5}$$ units

2 units

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

-0

The direction cosines $$\ell, \mathrm{m}, \mathrm{n}$$ of the line $$\frac{\mathrm{x}+2}{2}=\frac{2 \mathrm{y}-5}{3} ; \mathrm{z}=-1$$ are

$$\ell= \pm \frac{1}{\sqrt{5}}, \mathrm{~m}=0, \mathrm{n}= \pm \frac{2}{\sqrt{5}}$$

$$\ell= \pm \frac{3}{5}, \mathrm{~m}= \pm \frac{4}{5}, \mathrm{n}=0$$

$$\ell= \pm \frac{4}{5}, \mathrm{~m}= \pm \frac{3}{5}, \mathrm{n}=0$$

$$\ell= \pm \frac{1}{\sqrt{3}}, \mathrm{~m}= \pm \frac{1}{\sqrt{3}}, \mathrm{n}= \pm \frac{1}{\sqrt{3}}$$

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