Standard +0.8 This is a standard FP3 question on skew lines requiring vector methods: finding direction vectors, using the scalar triple product formula for distance between skew lines. While it involves multiple steps and 3D geometry (inherently harder than 2D), it's a textbook application of a known formula with straightforward arithmetic, making it moderately above average difficulty for A-level but routine for Further Maths students.
The line \(l_1\) passes through the points \((0, 0, 10)\) and \((7, 0, 0)\) and the line \(l_2\) passes through the points \((4, 6, 0)\) and \((3, 3, 1)\). Find the shortest distance between \(l_1\) and \(l_2\). [7]
The line $l_1$ passes through the points $(0, 0, 10)$ and $(7, 0, 0)$ and the line $l_2$ passes through the points $(4, 6, 0)$ and $(3, 3, 1)$. Find the shortest distance between $l_1$ and $l_2$. [7]
\hfill \mbox{\textit{OCR FP3 2010 Q1 [7]}}