1
COMEDK 2024 Morning Shift
+1
-0

The foot of the perpendicular from $$(2,4,-1)$$ to the line $$x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)$$ is

A
$$(-4,-1,-3)$$
B
$$(4,-1,-3)$$
C
$$(-4,-1,3)$$
D
$$(-4,1,-3)$$
2
COMEDK 2024 Morning Shift
+1
-0

$$P$$ is a point on the line segment joining the points $$(3,2,-1)$$ and $$(6,2,-2)$$. If $$x$$ coordinate of $$\mathrm{P}$$ is 5, then its $$y$$ co-ordinate is

A
2
B
0
C
5
D
$$-1$$
3
COMEDK 2024 Morning Shift
+1
-0

The vector equation of two lines are

\begin{aligned} & \vec{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k} \\ & \vec{r}=(s+1) \hat{\imath}+(2 s-1) \hat{\jmath}-(2 s+1) \hat{k} \end{aligned}

Then the shortest distance between them is

A
$$\frac{4}{29}$$
B
$$\frac{4}{\sqrt{29}}$$
C
$$\frac{8}{29}$$
D
$$\frac{8}{\sqrt{29}}$$
4
COMEDK 2023 Morning Shift
+1
-0

The place $$x-2 y+z=0$$ is parallel to the line

A
$$\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-3}{6}$$
B
$$\frac{x-2}{1}=\frac{y-2}{-2}=\frac{z-3}{1}$$
C
$$\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-4}{4}$$
D
$$\frac{x-4}{3}=\frac{y-5}{4}=\frac{z-6}{3}$$
EXAM MAP
Medical
NEET