NEB Class 12 3D Geometry: Vector Equations of Lines and Planes

Three-dimensional geometry in Class 12 Math carries 12 marks across straight lines and planes.

Shortest Distance Between Skew Lines

For lines $\vec{r} = \vec{a}_1 + \lambda \vec{b}_1$ and $\vec{r} = \vec{a}_2 + \mu \vec{b}_2$, the shortest distance is $d = \frac{|(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2)|}{|\vec{b}_1 \times \vec{b}_2|}$. Practice vector cross product determinants under timed conditions.