List of top Mathematics Questions on Three Dimensional Geometry asked in JKCET

What will be the distance of $ (1, 0, 2) $ from the point of intersection of plane $ x - y + z = 16 $ and the line $ \left(\frac{x-2}{3}\right) = \left(\frac{y+1}{4}\right) = \left(\frac{z-2}{12}\right) $ ?

If the plane $ 2x-3y+6z-11=0 $ makes an angle $ \theta $ with the $x-axis$, then the value of $ \tan \theta $ is equal to

If the image of the point $ (1,\,-2,3) $ in the plane $ 2x+3y-z=7 $ is the point $ (\alpha ,\beta ,\gamma ) $ then $ \alpha +\beta +\gamma $ is equal to

The shortest distance between the lines $ \frac{x}{-1}=\frac{y}{1}=\frac{z}{1} $ and $ \frac{x-3}{0}=\frac{y+3}{1}=\frac{z-3}{-1} $ is

Find the intersection of the spheres $ {{x}^{2}}+{{y}^{2}}+{{z}^{2}}+7x-2y-z=13 $ and $ {{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+3y+4z=8 $

Find the length of the diagonal of the parallelepiped formed by planes drawn through the points $ (2,3,5) $ and $ (5,9,7), $ parallel to the co-ordinate planes?

The angle between the two lines $ \frac{2-x}{1}=\frac{y}{2}=\frac{z+3}{1} $ and $ \frac{x-4}{4}=\frac{y-1}{1}=\frac{z-5}{2} $ is

The equation of the plane perpendicular to the $z$-axis and passing through $ (2,-3,5) $ is

The length of the perpendicular distance of the point $ (-1,\,4,\,0) $ from the line $ \frac{x}{1}=\frac{y}{3}=\frac{z}{1} $ is equal to

The number of lines making equal angles with the coordinate axes in three dimensional geometry is equal to

The projection of a line segment $OP$ through origin $O$, on the coordinate axes are $8, 5, 6$. Then, the length of the line segment $OP$ is equal to

The vector equation of the straight line $ 6x-8=2y-7=3z $ is

The unit normal vector to the plane $ 3x+2y-2z=8\sqrt{17} $ is

The radius of the sphere $ |\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3 $ is

The foot of the perpendicular drawn from the origin to a plane is $ (1,-1,5) $ . The equation of the plane is

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

If $ P=(0,1,2),\,\,Q=(4,-2,1),O=(0,0,0), $ then $ \angle POQ $ is equal to

Through the point $ P(\alpha ,\,\beta ,\,\,\gamma ) $ a plane is drawn at right angles to OP to meet the coordinate axes are A, B,. C respectively. If $ OP=p, $ then equation of plane $ ABC$ is

The direction cosines of two rays $ \overrightarrow{AB} $ and $ \overrightarrow{AC} $ are $ \left( \frac{1}{2},\frac{1}{2},-1 \right) $ and $ \left( \frac{2}{7},\frac{-3}{7},\frac{6}{7} \right). $ The direction ratios of one of the bisectors of angle $ \left( \overrightarrow{AB},\overrightarrow{AC} \right) $ are

If the foot of the perpendicular from $ (0,0,0) $ to a plane is $ (1,2,2), $ then the equation of the plane is

If a line makes angles $ \frac{\pi }{3} $ and $ \frac{\pi }{4} $ with the $x$ and $y$-axis respectively, then the angle made by the line and $Z$-axis is

The equation of the plane passing through the points $ (a,0,0),(0,b,0) $ and $ (0,0,c) $ is

The angle between the lines with direction ratios $ (4,-3,5) $ and $ (3,4,5) $ is