3D Geometry · JEE Main previous year questions

2023 57 questions

1. Q272023 · 25 Jan 2023 · Shift 2· Numerical answer

   If the shortest distance between the line joining the points (1, 2, 3) and (2, 3, 4), and the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-2}{0}$ is $\alpha$, then $28{\alpha }^2$ is equal to ____.

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   Answer: 18

2. Q162023 · 24 Jan 2023 · Shift 1

   The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

   1. A.$4\sqrt{2}$
   2. B.4
   3. C.5
   4. D.$5\sqrt{2}$
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   Answer: D

3. Q182023 · 24 Jan 2023 · Shift 1

   The distance of the point $(-1,9,-16)$ from the plane $2x+3y-z=5$ measured parallel to the line $\frac{x+4}{3}=\frac{2-y}{4}=\frac{z-3}{12}$ is :

   1. A.$13\sqrt{2}$
   2. B.26
   3. C.$20\sqrt{2}$
   4. D.31
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   Answer: B

4. Q222023 · 24 Jan 2023 · Shift 1· Numerical answer

   The shortest distance between the lines $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-6}{2}$ and $\frac{x-6}{3}=\frac{1-y}{2}=\frac{z+8}{0}$ is equal to ____

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   Answer: 14

5. Q152023 · 24 Jan 2023 · Shift 2

   If the foot of the perpendicular drawn from $(1,9,7)$ to the line passing through the point $(3,2,1)$ and parallel to the planes $x+2y+z=0$ and $3y-z=3$ is $(\alpha ,\beta ,\gamma )$, then $\alpha +\beta +\gamma$ is equal to :

   1. A.3
   2. B.1
   3. C.$-1$
   4. D.5
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   Answer: D

6. Q172023 · 24 Jan 2023 · Shift 2

   Let the plane containing the line of intersection of the planes ${\mathrm{P}}_1:x+(\lambda +4)y+z=1$ and ${\mathrm{P}}_2:2x+y+z=2$ pass through the points $(0,1,0)$ and $(1,0,1)$. Then the distance of the point $(2\lambda ,\lambda ,-\lambda )$ from the plane ${\mathrm{P}}_2$ is :

   1. A.$2\sqrt{6}$
   2. B.$3\sqrt{6}$
   3. C.$4\sqrt{6}$
   4. D.$5\sqrt{6}$
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   Answer: B

7. Q222023 · 24 Jan 2023 · Shift 2· Numerical answer

   If the shortest distance between the lines $\frac{x+\sqrt{6}}{2}=\frac{y-\sqrt{6}}{3}=\frac{z-\sqrt{6}}{4}$ and $\frac{x-\lambda }{3}=\frac{y-2\sqrt{6}}{4}=\frac{z+2\sqrt{6}}{5}$ is 6, then the square of sum of all possible values of $\lambda$ is :

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   Answer: 384