List of top Mathematics Questions on Three Dimensional Geometry asked in AP ECET BSc Mathematics

The equation of the plane passing through the midpoint of the line joining the points (1,2,3) and (3,4,5) and perpendicular to it is

Consider the planes: $P_{1}: 3x + 15y + 21z = 9$, $P_{2}: x - 3y - z = 5$, $P_{3}: 2x + 10y + 14z = 5$. Which of the following is TRUE?

The direction ratios of the line $x - y + z - 5 = 0 = x - 3y - 6$ are

If the line $\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-1}{-1}$ intersect the curve $xy = c^{2}$ in XY-plane than $c = $

Radius of the circle $x^{2} + y^{2} + z^{2} = 169, x - 2y + 2z = 15$ is}

The radius of the sphere $x^{2} + y^{2} + z^{2} + 2x - 4y + 6z + 1 = 0$ is}

If the plane $lx + my + nz = p$ touches the sphere $x^{2} + y^{2} + z^{2} = a^{2}$ then}

The angle between the tangent plane to the sphere $x^{2} + y^{2} + z^{2} = 9$ at the point (2,1,2) and the XY - plane is}

The distance between the point (1,2,3) and the sphere $x^{2} + y^{2} + z^{2} = 9$ is}

The plane XOZ divides the line joining of (1,-1,5) and (2,3,4) in the ratio $\lambda : 1$ then the value of $\lambda = $

Solution of $\frac{dx}{yz} = \frac{dy}{zx} = \frac{dz}{xy}$ is}

The radius of the sphere whose centre is \((4,4,-2)\) and which passes through origin is

If a plane passes through a fixed point \((a,b,c)\) and cuts the axes in \(A,B,C\), then the locus of the centre of the sphere \(OABC\) is

The equation of the sphere passing through \((1,0,0),(0,1,0),(0,0,1)\) and has its centre on the plane \(x+y+z=6\) is

The angle of intersection of the two spheres \(x^2+y^2+z^2+6y+2z+8=0\) and \(x^2+y^2+z^2+6x+8y+4z+20=0\) is

The distance between the planes \(2x+y+2z=8\) and \(4x+2y+4z+5=0\) is

The equation of the plane which is parallel to \(x+3y+5z+1=0\) and \(5\) units from the origin is

A plane which bisects the angle between the two given planes \(x+2y+2z-2=0\) and \(2x-y+2z-4=0\), passes through the point

The radical plane of the spheres \(x^2+y^2+z^2+4x-2y+2z+6=0\) and \(x^2+y^2+z^2+2x-4y-2z+6=0\) is

The equation of a plane containing the line of intersection of the planes \(2x-y-4=0\) and \(y+2z-4=0\), and passing through the point \((1,1,0)\), is

The angle in degrees between two vectors \(\vec a=\dfrac{\sqrt3}{2}\hat i+\dfrac{1}{2}\hat j\) and \(\vec b=-\dfrac{\sqrt3}{2}\hat i+\dfrac{1}{2}\hat j\) is