List of top Mathematics Questions on 3D Geometry asked in MET

A line passing through origin and is perpendicular to two given lines \(2x + y + 6 = 0\) and \(4x + 2y - 9 = 0\). The ratio in which the origin divides this line, is

The image of the point \(P(1,3,4)\) in the plane \(2x - y + z + 3 = 0\), is

Equation of the plane that contains the lines \(\mathbf{r} = (\hat{\mathbf{i}}+\hat{\mathbf{j}}) + \lambda(\hat{\mathbf{i}}+2\hat{\mathbf{j}}-\hat{\mathbf{k}})\) and \(\mathbf{r} = (\hat{\mathbf{i}}+\hat{\mathbf{j}}) + \mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2\hat{\mathbf{k}})\), is

The distance of the point \((3,8,2)\) from the line \(\frac{x-1}{2} = \frac{y-3}{4} = \frac{z-2}{3}\) measured parallel to the plane \(3x + 2y - 2z + 15 = 0\), is

The equation of the plane through the intersection of the planes \(x + y + z = 1\) and \(2x + 3y - z + 4 = 0\) and parallel to X-axis, is

If $f(x)=logₓ(log~x)$, then $f^\prime(x)$ at $x=e$ is

The locus of the equation $xy+yz=0$ is

The direction cosines of any normal to the xy-plane are

The tangent and normal to a rectangular hyperbola $xy=c²$ at a point cut off intercepts $a₁, a₂$ on one axis and $b₁, b₂$ on the other, then $a₁a₂ + b₁b₂$ is equal to