1
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
$$\frac{x-1}{-3}=\frac{y-2}{-5}=\frac{z-3}{4}$$
2
MHT CET 2022 11th August Evening Shift
+2
-0

The equation of the plane passing through the points $$(2,3,1),(4,-5,3)$$ and parallel to $$X$$-axis is

A
$$3 y+4 z=13$$
B
$$y-4 z=-1$$
C
$$2 y+4 z=19$$
D
$$y+4 z=7$$
3
MHT CET 2021 24th September Evening Shift
+2
-0

The equation of the plane which passes through (2, $$-$$3, 1) and is normal to the line joining the points (3, 4, $$-$$1) and (2, $$-$$1, 5) is given by

A
$$x+5 y-6 z+19=0$$
B
$$x-5 y+6 z-23=0$$
C
$$x+5 y+6 z+7=0$$
D
$$x-5 y-6 z-11=0$$
4
MHT CET 2021 24th September Evening Shift
+2
-0

If $$G(3,-5, r)$$ is the centroid of $$\triangle A B C$$, where $$A \equiv(7,-8,1), B \equiv(p, q, 5), C \equiv(q+1,5 p, 0)$$ are vertices of the triangle $$A B C$$, then the values of $$p, q, r$$ are respectively

A
$$-2,3,2$$
B
$$-4,5,4$$
C
$$6,5,4$$
D
$$2,-2,3$$
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