OCR Further Pure Core 1 2021 June — Question 4 5 marks

Exam BoardOCR
ModuleFurther Pure Core 1 (Further Pure Core 1)
Year2021
SessionJune
Marks5
TopicVectors: Cross Product & Distances
TypeShortest distance between two skew lines
DifficultyStandard +0.8 This is a Further Maths question requiring the skew lines distance formula involving cross product and dot product. While the formula application is systematic once known, it requires multiple vector operations (cross product, dot product, magnitude) and is beyond standard A-level content, placing it moderately above average difficulty.
Spec4.04i Shortest distance: between a point and a line
4 The equations of two non-intersecting lines, \(l _ { 1 }\) and \(l _ { 2 }\), are \(l _ { 1 } : \mathbf { r } = \left( \begin{array} { c } 1 \\ 2 \\ - 1 \end{array} \right) + \lambda \left( \begin{array} { c } 2 \\ 1 \\ - 2 \end{array} \right) \quad l _ { 2 } : \mathbf { r } = \left( \begin{array} { c } 2 \\ 2 \\ - 3 \end{array} \right) + \mu \left( \begin{array} { c } 1 \\ - 1 \\ 4 \end{array} \right)\).
Find the shortest distance between lines \(l _ { 1 }\) and \(l _ { 2 }\). 
4 The equations of two non-intersecting lines, $l _ { 1 }$ and $l _ { 2 }$, are\\
$l _ { 1 } : \mathbf { r } = \left( \begin{array} { c } 1 \\ 2 \\ - 1 \end{array} \right) + \lambda \left( \begin{array} { c } 2 \\ 1 \\ - 2 \end{array} \right) \quad l _ { 2 } : \mathbf { r } = \left( \begin{array} { c } 2 \\ 2 \\ - 3 \end{array} \right) + \mu \left( \begin{array} { c } 1 \\ - 1 \\ 4 \end{array} \right)$.\\
Find the shortest distance between lines $l _ { 1 }$ and $l _ { 2 }$.

\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q4 [5]}}
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