1
MHT CET 2022 11th August Evening Shift
+2
-0

The distance between parallel lines

$$\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$$ and

$$\frac{x}{2}=\frac{y}{-2}=\frac{z}{1}$$ is :

A
$$\frac{2 \sqrt{5}}{3}$$ units
B
$$\frac{\sqrt{5}}{3}$$ units
C
$$\frac{5 \sqrt{5}}{3}$$ units
D
$$\frac{4 \sqrt{5}}{3}$$ units
2
MHT CET 2022 11th August Evening Shift
+2
-0

A line makes the same angle '$$\alpha$$' with each of the $$x$$ and $$y$$ axes. If the angle '$$\theta$$', which it makes with the $$z$$-axis, is such that $$\sin ^2 \theta=2 \sin ^2 \alpha$$, then the angle $$\alpha$$ is

A
$$\left(\frac{\pi}{4}\right)$$
B
$$\left(\frac{\pi}{2}\right)$$
C
$$\left(\frac{\pi}{3}\right)$$
D
$$\left(\frac{\pi}{6}\right)$$
3
MHT CET 2022 11th August Evening Shift
+2
-0

A tetrahedron has verticles $$P(1,2,1), Q(2,1,3), R(-1,1,2)$$ and $$O(0,0,0)$$. Then the angle between the faces $$O P Q$$ and $$P Q R$$ is

A
$$\cos ^{-1}\left(\frac{17}{35}\right)$$
B
$$\cos ^{-1}\left(\frac{17}{31}\right)$$
C
$$\cos ^{-1}\left(\frac{19}{35}\right)$$
D
$$\cos ^{-1}\left(\frac{19}{31}\right)$$
4
MHT CET 2022 11th August Evening Shift
+2
-0

The Cartesian equation of a line passing through $$(1,2,3)$$ and parallel to $$x-y+2 z=5$$ and $$3 x+y+z=6$$ is

A
$$\frac{x-1}{-3}=\frac{y-2}{5}=\frac{z-3}{4}$$
B
$$\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{1}$$
C
$$\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-3}{1}$$
D
$$\frac{x-1}{-3}=\frac{y-2}{-5}=\frac{z-3}{4}$$
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