List of top Mathematics Questions on Three Dimensional Geometry asked in MHT CET

The equation of a plane containing the point \( (1, -1, 1) \) and parallel to the plane \[ 2x + 3y - 4z = 17 \text{ is} \]

The angle between the line \[ \frac{x - 1}{2} = \frac{y + 3}{1} = \frac{z + 7}{2} \] and the plane \[ \mathbf{r} \cdot (6\hat{i} - 2\hat{j} - 3\hat{k}) = 5 \] is

The direction cosines of a line which makes equal acute angles with the co-ordinate axes are

If a line in octant OXYZ makes equal angles with the coordinate axes, then

Evaluate \[ \int_0^1 \frac{x^2 - 2}{x^2 + 1} \, dx \]

If \( a = \sin 175^\circ + \cos 175^\circ \), then

The straight lines represented by the equation \( 9x^2 - 12xy + 4y^2 = 0 \) are

The distance of the point \( (7, 5, 2) \) from the plane \( 3x + 4y + 2z - 8 = 0 \) measured parallel to the line \( \frac{x - 1}{3} = \frac{y - 2}{6} = \frac{z + 1}{2} \) is

If \( 2f(x) = f'(x) \) and \( f(0) = 3 \), then the value of \( f(2) \) is

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

If \( A(0, 4, 0) \), \( B(0, 0, 3) \), and \( C(0, 4, 3) \) are the vertices of \( \Delta ABC \), then its incenter is:

The equation of the line passing through the points \( (3, 4, -7) \) and \( (6, -1, 1) \) is:

The co-ordinates of the foot of the perpendicular from the point \( (0, 2, 3) \) on the line
\[ \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3} \]

The equation of the plane through $(-1, 1 , 2 ) $ whose normal makes equal acute angles with co-ordinate axes is

If $A$ and $B$ are foot of perpendicular drawn from point $Q (a, b, c)$ to the planes $yz$ and $zx$, then equation of plane through the points $A, B$ and $O$ is ___________

Direction cosines of the line $\frac{x+2}{2} = \frac{2y-5}{3}, z = -1$ is

Consider the lines $L_1 : \frac{x + 1}{3} = \frac{y + 2}{1} = \frac{z + 1}{2}$ and $L_2 : \frac{x - 2}{1} = \frac{y + 2}{2} = \frac{z - 3}{3}$, then the unit vector perpendicular to both $L_1$ and $L_2$ is

A line with positive direction cosines passes through the point $P(2,-1,2)$ and makes equal angles with the co-ordinate axes. The line meets the plane $2x+y+z=9$ at point Q. The length of the line segment PQ equals