COMEDK 2025 Morning Shift | Three Dimensional Geometry Question 8 | Mathematics

The value of $\lambda$ for which the angle between lines $\vec{r}=\hat{\imath}+\hat{\jmath}+\hat{k}+p(2 \hat{\imath}+\hat{\jmath}+2 \hat{k})$ and $\vec{r}=(1+q) \hat{\imath}+(1+q \lambda) \hat{\jmath}+(1+q) \hat{k}$ is $\frac{\pi}{2}$

$-$4

$-$2

COMEDK 2024 Evening Shift

MCQ (Single Correct Answer)

-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

$$ \cos ^{-1}\left(\frac{4}{9}\right) $$

$$ \sin ^{-1}\left(\frac{4}{3}\right) $$

$$ \sin ^{-1}\left(\frac{\sqrt{5}}{3}\right) $$

$$ \frac{\pi}{2} $$

COMEDK 2024 Evening Shift

MCQ (Single Correct Answer)

-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

$$ \left(\frac{-5}{3}, \frac{-2}{3}, \frac{-19}{3}\right) $$

$$ \left(\frac{5}{3}, \frac{2}{3}, \frac{-19}{3}\right) $$

$$ \left(\frac{-5}{3}, \frac{2}{3}, \frac{19}{3}\right) $$

$$ \left(\frac{5}{3}, \frac{2}{3}, \frac{19}{3}\right) $$

COMEDK 2024 Evening Shift

MCQ (Single Correct Answer)

-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

Exactly three values

Exactly two values

Any number of values

Exactly one value

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