1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The measure of the angle between the lines $$x=k+1, \quad y=2 k-1, \quad z=2 k+3, \quad k \in R \quad$$ and $$\quad \frac{x-1}{2}=\frac{y+1}{1}=\frac{z-1}{-2}$$ is

A
$$ \cos ^{-1}\left(\frac{4}{9}\right) $$
B
$$ \sin ^{-1}\left(\frac{4}{3}\right) $$
C
$$ \sin ^{-1}\left(\frac{\sqrt{5}}{3}\right) $$
D
$$ \frac{\pi}{2} $$
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The co-ordinate of the foot of the perpendicular from $$P(1,8,4)$$ on the line joining $$R(0,-1,3)$$ and $$Q(2,-3,-1)$$ is

A
$$ \left(\frac{-5}{3}, \frac{-2}{3}, \frac{-19}{3}\right) $$
B
$$ \left(\frac{5}{3}, \frac{2}{3}, \frac{-19}{3}\right) $$
C
$$ \left(\frac{-5}{3}, \frac{2}{3}, \frac{19}{3}\right) $$
D
$$ \left(\frac{5}{3}, \frac{2}{3}, \frac{19}{3}\right) $$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the straight lines $$\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-t}$$ and $$\frac{x-1}{t}=\frac{y-4}{2}=\frac{z-5}{1}$$ are intersecting then $$t$$ can have

A
Exactly three values
B
Exactly two values
C
Any number of values
D
Exactly one value
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+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
$$(-4,1,-3)$$
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