3D Geometry

Showing 131-135 of 461 questions.

Page 27 of 93

JEE Main 2022 (Online) 27th July Morning ShiftQuestion 131

If the plane $P$ passes through the intersection of two mutually perpendicular planes $2x+ky-5z=1$ and $3kx-ky+z=5$, $k<3$ and intercepts a unit length on positive $x$-axis, then the intercept made by the plane $P$ on the $y$-axis is

3D Geometry

$\frac1{11}$$\frac5{11}$$6$$7$

JEE Main 2022 (Online) 28th June Morning ShiftQuestion 132

The acute angle between the planes $P_1$ and $P_2$, when $P_1$ and $P_2$ are the planes passing through the intersection of the planes $5x+8y+13z-29=0$ and $8x-7y+z-20=0$ and the points $(2,1,3)$ and $(0,1,2)$, respectively, is

3D Geometry

$\frac{\pi}{3}$$\frac{\pi}{4}$$\frac{\pi}{6}$$\frac{\pi}{12}$

JEE Main 2022 (Online) 28th June Evening ShiftQuestion 133

Let the plane $ax+by+cz=d$ pass through $(2,3,-5)$ and is perpendicular to the planes $2x+y-5z=10$ and $3x+5y-7z=12$. If $a,b,c,d$ are integers $d>0$ and $\gcd(|a|,|b|,|c|,d)=1$, then the value of $a+7b+c+20d$ is equal to :

3D Geometry

$18$$20$$24$$22$

JEE Main 2022 (Online) 28th June Morning ShiftQuestion 134

If two distinct points $Q,R$ lie on the line of intersection of the planes $-x+2y-z=0$ and $3x-5y+2z=0$ and $PQ=PR=\sqrt{18}$ where the point $P$ is $(1,-2,3)$, then the area of the triangle $PQR$ is equal to

3D Geometry

$\frac{2}{3}\sqrt{38}$$\frac{4}{3}\sqrt{38}$$\frac{8}{3}\sqrt{38}$$\sqrt{\frac{152}{3}}$

JEE Main 2020 (Online) 5th September Morning ShiftQuestion 135

If $(a,b,c)$ is the image of the point $(1,2,-3)$ in the line, $\frac{x+1}2=\frac{y-3}{-2}=\frac z{-1}$, then $a+b+c$ is equal to :

3D Geometry

$-1$$1$$2$$3$