1
MHT CET 2021 22th September Morning Shift
+2
-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

A
$$\frac{1}{\sqrt{5}}$$
B
3 units
C
$$\sqrt{5}$$ units
D
2 units
2
MHT CET 2021 21th September Evening Shift
+2
-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

A
$$\ell= \pm \frac{1}{\sqrt{5}}, \mathrm{~m}=0, \mathrm{n}= \pm \frac{2}{\sqrt{5}}$$
B
$$\ell= \pm \frac{3}{5}, \mathrm{~m}= \pm \frac{4}{5}, \mathrm{n}=0$$
C
$$\ell= \pm \frac{4}{5}, \mathrm{~m}= \pm \frac{3}{5}, \mathrm{n}=0$$
D
$$\ell= \pm \frac{1}{\sqrt{3}}, \mathrm{~m}= \pm \frac{1}{\sqrt{3}}, \mathrm{n}= \pm \frac{1}{\sqrt{3}}$$
3
MHT CET 2021 21th September Evening Shift
+2
-0

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

A
$$\mathrm{x-4y-z+3=0}$$
B
$$\mathrm{x+4y+5z-27=0}$$
C
$$\mathrm{x-4y-5z+23=0}$$
D
$$\mathrm{x-4y+z-7=0}$$
4
MHT CET 2021 21th September Evening Shift
+2
-0

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

A
$$\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$$
B
$$\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}$$
C
$$\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$$
D
$$\frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, \frac{4}{\sqrt{29}}$$
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