1
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
2
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
$$x-y+z=$$
3
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
$$(1,2,3)$$
4
MHT CET 2021 23th September Morning Shift
+2
-0

If A(3, 2, $$-$$1), B($$-$$2, 2, $$-$$3) and D($$-$$2, 5, $$-$$4) are the vertices of a parallelogram, then the area of the parallelogram is

A
286 sq. units
B
$$\sqrt{286}$$ sq. units
C
300 sq. units
D
$$\sqrt{300}$$ sq. units
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