JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 24th February Evening ShiftQuestion 56

The vector equation of the plane passing through the intersection of the planes $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=1$ and $\vec{r}\cdot\left(\hat{i}-2\hat{j}\right)=-2$, and the point $(1,0,2)$ is :

3D Geometry

$\vec{r}\cdot\left(3\hat{i}+7\hat{j}+3\hat{k}\right)=7$$\vec{r}\cdot\left(\hat{i}+7\hat{j}+3\hat{k}\right)=7$$\vec{r}\cdot\left(\hat{i}-7\hat{j}+3\hat{k}\right)=\frac{7}{3}$$\vec{r}\cdot\left(\hat{i}+7\hat{j}+3\hat{k}\right)=\frac{7}{3}$

JEE Main 2023 (Online) 8th April Evening ShiftQuestion 57

Let $P$ be the plane passing through the line $\frac{x-1}{1}=\frac{y-2}{-3}=\frac{z+5}{7}$ and the point $(2,4,-3)$. If the image of the point $(-1,3,4)$ in the plane $P$ is $(\alpha,\beta,\gamma)$ then $\alpha+\beta+\gamma$ is equal to

3D Geometry

$9$$10$$11$$12$

JEE Main 2021 (Online) 25th February Evening ShiftQuestion 58

A plane passes through the points $A(1,2,3)$, $B(2,3,1)$ and $C(2,4,2)$. If $O$ is the origin and $P$ is $(2,-1,1)$, then the projection of $\overrightarrow{OP}$ on this plane is of length :

3D Geometry

$\sqrt{\frac{2}{3}}$$\sqrt{\frac{2}{11}}$$\sqrt{\frac{2}{7}}$$\sqrt{\frac{2}{5}}$

JEE Main 2023 (Online) 11th April Morning ShiftQuestion 59

Let $(\alpha,\beta,\gamma)$ be the image of the point $P(2,3,5)$ in the plane $2x+y-3z=6$. Then $\alpha+\beta+\gamma$ is equal to

3D Geometry

$12$$10$$9$$5$

JEE Main 2022 (Online) 24th June Evening ShiftQuestion 60

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 $\frac{1}{\sqrt{3}}$, then the sum of all possible values of $\lambda$ is:

3D Geometry

$16$$6$$12$$15$