MHT CET 2021 22th September Evening Shift | Three Dimensional Geometry Question 65 | Mathematics

A line drawn from a point $$A(-2,-2,3)$$ and parallel to the line $$\frac{x}{-2}=\frac{y}{2}=\frac{z}{-1}$$ meets the $$\mathrm{YOZ}$$ plane in point $$\mathrm{P}$$, then the co-ordinates of the point $$\mathrm{P}$$ are

$$(0,4,-4)$$

$$(0,2,2)$$

$$(0,-2,2)$$

$$(0,-4,4)$$

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

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

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

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

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

MHT CET 2021 21th September Evening Shift

MCQ (Single Correct Answer)

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The co-ordinates of the point $$\mathrm{P} \equiv(1,2,3)$$ and $$\mathrm{O} \equiv(0,0,0)$$, then the direction cosines of $$\overline{\mathrm{OP}}$$ are

$$\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$$

$$\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}$$

$$\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$$

$$\frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, \frac{4}{\sqrt{29}}$$

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