Three-Dimensional Geometry: JEE Main Mathematics Previous Year Questions

471 previous year questions from Three-Dimensional Geometry. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.Let the point, on the line passing through the points $P\text{(}1\text{,}-2\text{,}3\text{)}$ and $Q\text{(}5\text{,}-4\text{,}7\text{)}$, farther from the origin and a…
2. 2.The mirror image of $P\text{(}2\text{,}4\text{,}-1\text{)}$ in the plane $x-y$ $+2z-2=0$ is $\text{(}a\text{,}b\text{,}c\text{)}$, then the value of $a+b+c$ is
3. 3.If the equation of the plane passing through the point $\left(1\text{,}1\text{,}2\right)$ and perpendicular to the line $x-3y+2z-1=04x-y+z$ os…
4. 4.If a plane meets the coordinate axes at $A$, $B$ and $C$ in such a way that the centroid of triangle $\text{ABC}$ is at the point…
5. 5.The shortest distance between the lines $\frac{x-5}{1}=\frac{y-2}{2}=\frac{z-4}{-3}$ and $\frac{x+3}{1}=\frac{y+4}{4}=\frac{z-1}{-5}$
6. 6.If the line passing through the points $\text{(}5\text{,}1\text{,}a\text{)}$ and $\text{(}3\text{,}b\text{,}1\text{)}$ crosses the YZ plane at the point…
7. 7.Let $a=i+2j+k$ and $b=2i+7j+3k$. Let $L_1\text{:}r=(-i+2j+k)+\lambda a\text{,}\lambda \text{∈}R$ and $L_2\text{:}r$…
8. 8.A plane cuts the coordinate axes $X\text{,}Y\text{,}Z$ at $A\text{,}B\text{,}C$ respectively such that the centroid of the $\text{△}\text{ABC}$ is…
9. 9.If the distance of point $2i+3j+\lambda k$ from the plane $r\cdot \text{(}3i+2j+6k\text{)}=13$ is 5 units then $\lambda =$
10. 10.Let the plane P : 4x - y + z = 10 be rotated by an angle $\frac{\pi }{2}$ about its line of intersection with the plane x + y - z = 4. If $\alpha$ is the distance of the point (2…
11. 11.The shortest distance between the skew lines $r=\text{(}6i+2j+2k\text{)}+t\text{(}i-2j+2k\text{)}$ and $r=\text{(}-4i-k\text{)}+s\text{(}3i-2j-2k\text{)}$ is
12. 12.For real numbers α and β ≠ 0, if the point of intersection of the straight lines $\frac{x-\alpha }{1}=\frac{y-1}{2}=\frac{z-1}{3}$ and…
13. 13.The distance of the point $\text{(}1\text{,}2\text{,}1\text{)}$ from the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{2}$ is
14. 14.If $A$ and $B$ are foot of perpendicular drawn from point $Q\text{(}a\text{,}b\text{,}c\text{)}$ to the planes $\text{yz}$ and $\text{zx}$, then equation of plane th…
15. 15.A plane which bisects the angle between the two given planes $2x-y+2z-4=0$ and $x+2y+2z-2=0$ passes through the point :
16. 16.Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane $5y+8=0$.
17. 17.Let $L_1\text{:}\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-1}{2}$ and $L_2\text{:}\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z}{1}$ be two lines. Let $L_3$ be a line pas…
18. 18.If $\text{(}2\text{,}-1\text{,}2\text{)}$ and $\text{(}K\text{,}3\text{,}5\text{)}$ are the triads of direction ratios of two lines and the angle between them is…
19. 19.A line $L$ is parallel to both the planes $2x+3y+z=1$ and $x+3y+2z=2$. If line $L$ makes an angle $\alpha$ with the positive direction of X -axis, then…
20. 20.If the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda }$ and $\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{3}}$,…
21. 21.The equation of the plane through the points $\text{(}2\text{,}1\text{,}0\text{)}\text{,}\text{(}3\text{,}2\text{,}-2\text{)}$ and $\text{(}3\text{,}1\text{,}7\text{)}$…
22. 22.The coordinates of the point $\text{(}3\text{,}-7\text{,}5\text{)}$ in the new system, when the origin is shifted to the point $\text{(}-1\text{,}-1\text{,}-1\text{)}$…
23. 23.A point on the plane that passes through the points $\text{(}1\text{,}-1$, $6\text{)}\text{,}\text{(}0\text{,}0\text{,}7\text{)}$ and perpendicular to the plane…
24. 24.The mid points of the sides of triangle are $\text{(}1\text{,}5\text{,}-1\text{)}\text{,}\text{(}0\text{,}4\text{,}-2\text{)}$ and $\text{(}2\text{,}3\text{,}4\text{)}$…
25. 25.If the line passes through the points $P\text{(}6\text{,}-1\text{,}2\text{)}$, $Q\text{(}8\text{,}-7\text{,}2\lambda \text{)}$ and…