3D Geometry

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JEE Main 2014 (Online) 9th AprilQuestion 211

Equation of the plane which passes through the point of intersection of lines $\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ and has the largest distance from the origin is :

3D Geometry

$4x+3y+5z=50$$3x+4y+5z=49$$5x+4y+3z=57$$7x+2y+4z=54$

JEE Main 2014 (Online) 9th AprilQuestion 212

A line in the $3$-dimensional space makes an angle $\theta\ \left(0<\theta\le\frac\pi2\right)$ with both the $X$ and $Y$-axes. Then, the set of all values of $\theta$ is in the interval :

3D Geometry

$\left(\frac\pi3,\frac\pi2\right]$$\left(0,\frac\pi4\right]$$\left[\frac\pi4,\frac\pi2\right]$$\left[\frac\pi6,\frac\pi3\right]$

JEE Main 2014 (Online) 11th AprilQuestion 213

The plane containing the line $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and parallel to the line $\frac x1=\frac y1=\frac z4$ passes through the point :

3D Geometry

$(1,-2,5)$$(1,0,5)$$(0,3,-5)$$(-1,-3,0)$

AIEEE 2003 (Offline)Question 214

A tetrahedron has vertices at $O(0,0,0)$, $A(1,2,1)$, $B(2,1,3)$ and $C(-1,1,2)$. Then the angle between the faces $OAB$ and $ABC$ will be :

3D Geometry

$90^\circ$$\cos^{-1}\left(\frac{19}{35}\right)$$\cos^{-1}\left(\frac{17}{31}\right)$$30^\circ$

AIEEE 2007 (Offline)Question 215

If a line makes an angle of $\pi/4$ with the positive directions of each of $x$-axis and $y$-axis, then the angle that the line makes with the positive direction of the $z$-axis is :

3D Geometry

$\frac\pi4$$\frac\pi2$$\frac\pi6$$\frac\pi3$