Geometry PYQ — Page 7

The sum of all the values of $\lambda$ for which the distance of the point P (2, 3, $\lambda$) from the plane $x + 2y - 2z = 9$ is 3 units, is

The value of $\sin\left[\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]$ is :

Match List - I with List - II. | List - I | List - II | |---|---| | (A) $\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$ | (I) $\frac{3\pi}{4}$ | | (B) $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$ | (II) $-\frac{\pi}{3}$ | | (C) $\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)$ | (III) $\frac{\pi}{2}$ | | (D) $\cos^{-1}\left(\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right)$ | (IV) $\frac{2\pi}{3}$ | Choose the correct answer from the options given below :

The direction ratio's of line of intersection of two planes : $2x + y + z + 47 = 0$ and $3x - 2y - z + 41 = 0$ are :

A line makes angle $\theta$ with $x$-axes as well as $z$-axis. If the angle $\beta$, which it makes with $y$-axis is such that $\sin^2\beta = 3\sin^2\theta$, then $\cos^2\theta$ is :

The equation of the plane, parallel to the plane $3x + 4y - 12z = 3$ and passes through $(1, 1, -1)$, is :

The distance of plane $\vec{r}\cdot(6\hat{i} - 3\hat{j} - 2\hat{k}) + 1 = 0$ from origin is :

The foot of perpendicular from point $(2, 4, -1)$ on the line $\frac{x+5}{1} = \frac{y+3}{4} = \frac{z-6}{-9}$ is :

Find the root of perpendicular from origin to the line $\frac{x - 1}{3} = \frac{y - 2}{-2} = \frac{z + 1}{3}$.

The distance of the point $(2, 3, -5)$ from the plane $x + 2y - 2z = 9$ is :

Equation of y-axis in space, in vector form is :

The equation of plane that contains line $\frac{x - 1}{-1} = \frac{y + 1}{2} = \frac{z - 1}{3}$ and also pass through point $(0, 1, 0)$ is :

The value of $\cos^{-1} \left( \sin \left( \cos^{-1} \frac{1}{2} \right) \right) + \tan^{-1}(1)$

The angle between 2 planes $4x + 8y + z - 8 = 0$ and $y + z - 4 = 0$ is :