Zero Component Vectors in 3D

00:00 3 marks

  • Build Confidence
  • HL
  • Tier 2
  • Form lines in 2D/3D with zero components in the direction vector

Given the point \(P(3, -2, 5)\) and the direction vector \(d = (0, 4, 0)\), write the vector equation of the line through \(P\) that is parallel to \(d\).

Hint Hint

Hint

Recall that the vector equation of a line is given by \(r = P + t\,d\), where \(t\) is a real number.

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Complete Answer

The line is given by \(r(t) = (3, -2, 5) + t(0, 4, 0)\), where \(t \in \mathbb{R}\).

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