3D Geometry · JEE Advanced previous year questions

7 questions asked across 3 exam years, newest first

2024 2 questions

Q122024 · 26 May 2024 · Paper 1· Numerical answer
Let $\overline{O P} = \frac{α - 1}{α} \hat{i} + \hat{j} + \hat{k}$ , $\overline{O Q} = \hat{i} + \frac{β - 1}{β} \hat{j} + \hat{k}$ and $\overline{O R} = \hat{i} + \hat{j} + \frac{1}{2} \hat{k}$ be three vectors, where $α, β \in R - {0}$ and $O$ denotes the origin. If $(\overline{O P} \times \overline{O Q}) \cdot \overline{O R} = 0$ and the point $(α, β, 2)$ lies on the plane $3 x + 3 y - z + l = 0$ , then the value of $l$ is _____.
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Answer: 5
Q72024 · 26 May 2024 · Paper 2· One or more correct
Let $A_{1}, B_{1}, C_{1}$ be three points in the $x y$ -plane. Suppose that the lines $A_{1} C_{1}$ and $B_{1} C_{1}$ are tangents to the curve $y^{2} = 8 x$ at $A_{1}$ and $B_{1}$ , respectively. If $O = (0, 0)$ and $C_{1} = (- 4, 0)$ , then which of the following statements is (are) TRUE?
1. A.The length of the line segment $O A_{1}$ is $43$
2. B.The length of the line segment $A_{1} B_{1}$ is 16
3. C.The orthocenter of the triangle $A_{1} B_{1} C_{1}$ is $(0, 0)$
4. D.The orthocenter of the triangle $A_{1} B_{1} C_{1}$ is $(1, 0)$
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Answer: A, C