1
MHT CET 2021 24th September Morning Shift
+2
-0

If $$\mathrm{A}$$ and $$\mathrm{B}$$ are the foot of the perpendicular drawn from the point $$\mathrm{Q}(\mathrm{a}, \mathrm{b}, \mathrm{c})$$ to the planes $$\mathrm{YZ}$$ and $$\mathrm{ZX}$$ respectively, then the equation of the plane through the points $$\mathrm{A}, \mathrm{B}$$, and $$\mathrm{O}$$ is (where $$\mathrm{O}$$ is the origin)

A
$$\frac{x}{a}-\frac{y}{b}-\frac{z}{c}=0$$
B
$$\frac{x}{a}+\frac{y}{b}-\frac{z}{c}=0$$
C
$$\frac{x}{a}-\frac{y}{b}+\frac{z}{c}=0$$
D
$$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=0$$
2
MHT CET 2021 24th September Morning Shift
+2
-0

If $$\mathrm{A}=(-2,2,3), \mathrm{B}=(3,2,2), \mathrm{C}=(4,-3,5)$$ and $$\mathrm{D}=(7,-5,-1)$$ Then the projection of $$\overline{\mathrm{AB}}$$ on $$\overline{\mathrm{CD}}$$ is

A
4
B
3
C
$$\frac{12}{\sqrt7}$$
D
None of these
3
MHT CET 2021 23rd September Evening Shift
+2
-0

The Cartesian equation of a plane which passes through the points $$\mathrm{A}(2,2,2)$$ and making equal nonzero intercepts on the co-ordinate axes is

A
$$x+y+z=6$$
B
$$x-2 y+z=0$$
C
$$2 x+y+z=7$$
D
$$x-y+z=$$
4
MHT CET 2021 23rd September Evening Shift
+2
-0

The co-ordinates of the foot of the perpendicular drawn from the point $$2 \hat{i}-\hat{j}+5 \hat{k}$$ to the line $$\vec{r}=(11 \hat{i}-2 \hat{j}-8 \hat{k})+\lambda(10 \hat{i}-4 \hat{j}-11 \hat{k})$$ are

A
$$(1,-2,3)$$
B
$$(1,2,-3)$$
C
$$(-1,2,3)$$
D
$$(1,2,3)$$
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