WB JEE 2026 | Three Dimensional Geometry Question 1 | Mathematics

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

The point of intersection of $\vec{r} \times \vec{a}=\vec{b} \times \vec{a}$ and $\vec{r} \times \vec{b}=\vec{a} \times \vec{b}$, where $\vec{a}=\hat{i}+\hat{j}$ and $\vec{b}=2 \hat{i}-\hat{k}$ is

$3 \hat{i}+2 \hat{j}+\hat{k}$

$\hat{i}-\hat{j}-\hat{k}$

$4 \hat{i}+2 \hat{j}-\hat{k}$

$3 \hat{i}+\hat{j}-\hat{k}$

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

Intercepts of the plane $\vec{r} \cdot \vec{n}=d(\neq 0)$ on the coordinate axes respectively are

$\frac{\hat{i} \cdot \vec{n}}{d}, \frac{\hat{j} \cdot \vec{n}}{d}, \frac{\hat{k} \cdot \vec{n}}{d}$

$\left|\frac{\hat{i} \cdot \hat{n}}{d}\right|,\left|\frac{\hat{j} \cdot \vec{n}}{d}\right|,\left|\frac{\hat{k} \cdot \vec{n}}{d}\right|$

$\frac{d}{\hat{i} \cdot \hat{n}}, \frac{d}{\hat{j} \cdot \hat{n}}, \frac{d}{\hat{k} \cdot \hat{n}}$

$\frac{d}{\hat{i} \cdot \vec{n}}, \frac{d}{\hat{j} \cdot \vec{n}}, \frac{d}{\hat{k} \cdot \vec{n}}$

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

Consider a square $A B C D$ of diagonal length 2a. The square is folded along the diagonal $A C$ so that the plane of $\triangle A B C$ is perpendicular to the plane of $\triangle A D C$. In this case the shortest distance between $A B$ and $C D$ is

$\frac{2 a}{\sqrt{3}}$

$\frac{a}{2 \sqrt{3}}$

$\frac{\mathrm{a}}{\sqrt{3}}$

$\frac{\sqrt{3} a}{2}$

WB JEE 2025

MCQ (Single Correct Answer)

-0.25

The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$ is

parallel to the $x$-axis.

parallel to the $y$-axis.

parallel to the $z$-axis.

perpendicular to the $z$-axis.

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