JEE Maths PYQ Practice, chapter-wise

JEE Main 2016 (Offline)Question 276

If the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane $lx+my-z=9$, then $l^{2}+m^{2}$ is equal to

3D Geometry

$5$$2$$26$$18$

JEE Main 2019 (Online) 12th April Morning ShiftQuestion 277

If the line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the plane $2x+3y-z+13=0$ at a point $P$ and the plane $3x+y+4z=16$ at a point $Q$, then $PQ$ is equal to

3D Geometry

$2\sqrt7$$14$$2\sqrt{14}$$\sqrt{14}$

JEE Main 2021 (Online) 1st September Evening ShiftQuestion 278

Let the acute angle bisector of the two planes $x-2y-2z+1=0$ and $2x-3y-6z+1=0$ be the plane $P$. Then which of the following points lies on $P$ ?

3D Geometry

$(0,2,-4)$$\left(-2,0,-\frac12\right)$$(4,0,-2)$$\left(3,1,-\frac12\right)$

JEE Advanced 2019 Paper 1Question 279

Let $L_1$ and $L_2$ denote the lines $$\vec r=\hat i+\lambda(-\hat i+2\hat j+2\hat k),\ \lambda\in\mathbb{R}\ \text{and}$$ $$\vec r=\mu(2\hat i-\hat j+2\hat k),\ \mu\in\mathbb{R}$$ respectively. If $L_3$ is a line which is perpendicular to both $L_1$ and $L_2$ and cuts both of them, then which of the following options describe(s) $L_3$?

3D Geometry

More than one option may be correct.

$\vec r=\frac{2}{9}(4\hat i+\hat j+\hat k)+t(2\hat i+2\hat j-\hat k),\ t\in\mathbb{R}$$\vec r=\frac{2}{9}(2\hat i-\hat j+2\hat k)+t(2\hat i+2\hat j-\hat k),\ t\in\mathbb{R}$$\vec r=\frac{1}{3}(2\hat i+\hat k)+t(2\hat i+2\hat j-\hat k),\ t\in\mathbb{R}$$\vec r=t(2\hat i+2\hat j-\hat k),\ t\in\mathbb{R}$

JEE Main 2019 (Online) 12th April Evening ShiftQuestion 280

The length of the perpendicular drawn from the point $(2,1,4)$ to the plane containing the lines $\vec r=(\hat i+\hat j)+\lambda(\hat i+2\hat j-\hat k)$ and $\vec r=(\hat i+\hat j)+\mu(-\hat i+\hat j-2\hat k)$ is

3D Geometry

$\frac13$$3$$\sqrt3$$\frac1{\sqrt3}$