# Three Dimensional Geometry · Mathematics · COMEDK

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COMEDK 2024 Evening Shift
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 $$\quad \frac{x-1}{2}=\frac{y+1}{1}=\frac{... COMEDK 2024 Evening Shift The co-ordinate of the foot of the perpendicular from$$P(1,8,4)$$on the line joining$$R(0,-1,3)$$and$$Q(2,-3,-1)$$is COMEDK 2024 Evening Shift If the straight lines$$\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$$can... COMEDK 2024 Morning Shift The foot of the perpendicular from$$(2,4,-1)$$to the line$$x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)$$is COMEDK 2024 Morning Shift$$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$$co-o... COMEDK 2024 Morning Shift The vector equation of two lines are$$\begin{aligned} & \vec{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k} \\ & \vec{r}=(s+1) \hat{\imath}...
COMEDK 2023 Morning Shift
The place $$x-2 y+z=0$$ is parallel to the line
COMEDK 2023 Morning Shift
The lines $$\frac{x-1}{2}=\frac{y-4}{4}=\frac{z-2}{3}$$ and $$\frac{1-x}{1}=\frac{y-2}{5}=\frac{3-z}{a}$$ are perpendicular to each other, then $$a$$ ...
COMEDK 2023 Morning Shift
If two lines $$L_1: \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$$ and $$L_2: \frac{x-3}{1}=\frac{y-k}{2}=z$$ intersect at a point, then $$2 k$$ is equal...
COMEDK 2023 Evening Shift
If the direction ratios of two lines are given by $$3 l m-4 l n+m n=0$$ and $$l+2 m+3 n=0$$, then the angle between the lines is
COMEDK 2023 Evening Shift
The coordinates of the vertices of the triangle are $$A(-2,3,6), B(-4,4,9)$$ and $$C(0,5,8)$$. The direction cosines of the median $$\mathrm{BE}$$ are...
COMEDK 2023 Evening Shift
$$\mathrm{P} \text { is a point on the line segment joining the points }(3,2,-1) \text { and }(6,2,-2) \text {. If the } x \text { co ordinate of } \... COMEDK 2023 Evening Shift The distance of the point$$(2,3,4)$$from the line$$1-x=\frac{y}{2}=\frac{1}{3}(1+z)$$is COMEDK 2023 Evening Shift If the position vector of a point$$A$$is$$\vec{a}+2 \vec{b}$$and$$\vec{a}$$divides$$A B$$in the ratio$$2: 3$$, then the position vector of$$...
COMEDK 2022
The line $$\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-5}{6}$$ is parallel to the plane
COMEDK 2022
The angle between the lines $${{x + 4} \over 3} = {{y - 1} \over 5} = {{z + 3} \over 4}$$ and $${{x + 1} \over 1} = {{y - 4} \over 1} = {{z - 5} \over... COMEDK 2022 The point of intersection of the lines$${{x - 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}$$and$${{x -5} \over 2} = {{y - 2} \over 1} = z$$... COMEDK 2021 The line$${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$is parallel to the plane COMEDK 2021 The equation of a plane passing through the line of intersection of the planes$$x+2y+3z=2,x-y+z=3$$and at a distance$$\frac{2}{\sqrt3}$$from the p... COMEDK 2021 The angle between the lines$$2x=3y=-z$$and$$6x=-y=-4z$$is COMEDK 2021 The point of intersection of the lines$${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}$$and$${{x - 4} \over 5} = {{y - 1} \over 2} = z$$... COMEDK 2020 A vector perpendicular to the plane containing the points$$A(1, - 1,2),B(2,0, - 1),C(0,2,1) is
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