MHT CET 2021 22th September Morning Shift | Three Dimensional Geometry Question 85 | Mathematics

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)

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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)

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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

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

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

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

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

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

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Equation of the plane passing through the point (2, 0, 5) and parallel to the vectors $$\widehat i - \widehat j + \widehat k$$ and $$3\widehat i + 2\widehat j - \widehat k$$ is

$$\mathrm{x-4y-z+3=0}$$

$$\mathrm{x+4y+5z-27=0}$$

$$\mathrm{x-4y-5z+23=0}$$

$$\mathrm{x-4y+z-7=0}$$

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