1
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
$$(1,2,3)$$
2
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
3
MHT CET 2021 23th September Morning Shift
+2
-0

The distance between the parallel lines $$\frac{x-2}{3}=\frac{y-4}{5}=\frac{z-1}{2}$$ and $$\frac{x-1}{3}=\frac{y+2}{5}=\frac{z+3}{2}$$ is

A
$$\frac{1}{\sqrt{38}}$$ units
B
$$\sqrt{\frac{333}{38}}$$ units
C
$$\sqrt{\frac{300}{37}}$$ units
D
$$\sqrt{\frac{300}{35}}$$ units
4
MHT CET 2021 23th September Morning Shift
+2
-0

The coordinates of the foot of the perpendicular drawn from the origin to the plane $$2 x+y-2 z=18$$ are

A
$$(4,2,-4)$$
B
$$(1,2,-3)$$
C
$$(4,2,4)$$
D
$$(4,-2,-4)$$
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