Vector equation of a line

Questions asking to write or convert the equation of a line in vector form r = a + λb, given points or other information.

2 questions · Standard +0.0

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CAIE P3 2016 March Q8
9 marks Standard +0.3
8 The line \(l\) has equation \(\mathbf { r } = \left( \begin{array} { r } 1 \\ 2 \\ - 1 \end{array} \right) + \lambda \left( \begin{array} { l } 2 \\ 1 \\ 3 \end{array} \right)\). The plane \(p\) has equation \(\mathbf { r } \cdot \left( \begin{array} { r } 2 \\ - 1 \\ - 1 \end{array} \right) = 6\).
  1. Show that \(l\) is parallel to \(p\).
  2. A line \(m\) lies in the plane \(p\) and is perpendicular to \(l\). The line \(m\) passes through the point with coordinates (5, 3, 1). Find a vector equation for \(m\).
OCR Further Pure Core AS 2018 June Q1
5 marks Moderate -0.3
1
  1. Find a vector which is perpendicular to both \(\left( \begin{array} { r } 1 \\ 3 \\ - 2 \end{array} \right)\) and \(\left( \begin{array} { r } - 3 \\ - 6 \\ 4 \end{array} \right)\).
  2. The cartesian equation of a line is \(\frac { x } { 2 } = y - 3 = 2 z + 4\). Express the equation of this line in vector form.