Three Dimensional Geometry

JEE Main · Mathematics · 17 past questions

These are the board's own papers. 314 more board questions reprinted in the books we use in class are for signed-in students: sign in.

1. Q1 2026 2 Apr Shift 1

   If the point of intersection of the lines $\dfrac{x+1}{3}=\dfrac{y+a}{5}=\dfrac{z+b+1}{7}$ and…

   Try it →
2. Q2 2026 2 Apr Shift 1

   Let a line $L$ passing through the point $(1, 1, 1)$ be perpendicular to both the vectors…

   Try it →
3. Q3 2026 2 Apr Shift 2

   Let the point A be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line…

   Try it →
4. Q4 2026 4 Apr Shift 1

   A line with direction ratios $1, -1, 2$ intersects the lines $\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3}$ and…

   Try it →
5. Q5 2026 4 Apr Shift 1

   The square of the distance of the point $(-2, -8, 6)$ from the line…

   Try it →
6. Q6 2026 4 Apr Shift 2

   The shortest distance between the lines…

   Try it →
7. Q7 2026 4 Apr Shift 2

   If $\left(2\alpha+1,\alpha^2-3\alpha,\frac{\alpha-1}{2}\right)$ is the image of $(\alpha,2\alpha,1)$ in the…

   Try it →
8. Q8 2026 5 Apr Shift 1

   The square of the distance of the point $P(5, 6, 7)$ from the line…

   Try it →
9. Q9 2026 5 Apr Shift 1

   The square of the distance of the point of intersection of the lines…

   Try it →
10. Q10 2026 5 Apr Shift 2

    Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8} = \frac{y-4}{2} = \frac{z+1}{2}$ and…

    Try it →
11. Q11 2026 5 Apr Shift 2

    If the distance of the point (a, 2, 5) from the image of the point (1, 2, 7) in the line…

    Try it →
12. Q12 2026 6 Apr Shift 1

    Let the image of the point $P(1,6,a)$ in the line $L:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}, b>0,$ be…

    Try it →
13. Q13 2026 6 Apr Shift 1

    Let a line L be perpendicular to both the lines $L_1:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and…

    Try it →
14. Q14 2026 6 Apr Shift 2

    The shortest distance between the lines $\dfrac{x-4}{1}=\dfrac{y-3}{2}=\dfrac{z-2}{-3}$ and…

    Try it →
15. Q15 2026 6 Apr Shift 2

    Let the image of the point $P(0,-5,0)$ in the line $\dfrac{x-1}{2}=\dfrac{y}{1}=\dfrac{z+1}{-2}$ be the point…

    Try it →
16. Q16 2026 8 Apr Shift 2

    Let the foot of perpendicular from the point (λ, 2, 3) on the line (x-4)/1 = (y-9)/2 = (z-5)/1 be the point…

    Try it →
17. Q17 2026 8 Apr Shift 2

    Let a line $L_1$ pass through the origin and be perpendicular to the lines…

    Try it →