3D Geometry · JEE Main previous year questions

2022 28 questions

1. Q162022 · 25 Jun 2022 · Shift 2

   Let $\mathrm{p}$ be the plane passing through the intersection of the planes $\vec{r}\cdot (\hat{i}+3\hat{j}-\hat{k})=5$ and $\vec{r}\cdot (2\hat{i}-\hat{j}+\hat{k})=3$, and the point $(2,1,-2)$. Let the position vectors of the points $\mathrm{X}$ and $\mathrm{Y}$ be $\hat{i}-2\hat{j}+4\hat{k}$ and $5\hat{i}-\hat{j}+2\hat{k}$ respectively. Then the points :

   1. A.X and X + Y are on the same side of P
   2. B.Y and Y - X are on the opposite sides of P
   3. C.X and Y are on the opposite sides of P
   4. D.X + Y and X - Y are on the same side of P
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   Answer: C

2. Q292022 · 25 Jun 2022 · Shift 2· Numerical answer

   Let ${\mathrm{l}}_1$ be the line in xy-plane with x and y intercepts $\frac{1}{8}$ and $\frac{1}{4\sqrt{2}}$ respectively, and ${\mathrm{l}}_2$ be the line in zx-plane with x and z intercepts $-\frac{1}{8}$ and $-\frac{1}{6\sqrt{3}}$ respectively. If d is the shortest distance between the line ${\mathrm{l}}_1$ and ${\mathrm{l}}_2$, then $d^{-2}$ is equal to $\underline{}$.

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   Answer: 51

3. Q182022 · 24 Jun 2022 · Shift 2

   Let the points on the plane P be equidistant from the points $(-4,2,1)$ and $(2,-2,3)$. Then the acute angle between the plane P and the plane $2x+y+3z=1$ is :

   1. A.$\frac{\pi }{6}$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{3}$
   4. D.$\frac{5\pi }{12}$
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   Answer: C