3D Line Vector Representation

00:00 3 marks

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  • SL & HL
  • Tier 2
  • Vectors
  • Parametric equations
  • 3D geometry

Given a point \(P(2, -1, 3)\) and a direction vector \(\vec{d} = \langle 4, 0, -2 \rangle\), write the vector equation of the line passing through \(P\) in 3D space.

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Hint

Recall that the vector equation is given by \(\vec{r} = \vec{r_0} + t\vec{d}\), where \(\vec{r_0}\) is the position vector of point \(P\).

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Complete Answer

The line can be represented as \(\vec{r} = \langle 2, -1, 3 \rangle + t\langle 4, 0, -2 \rangle\).

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