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  • A-Level Further Maths

Vectors

The equation of a line can be represented by vectors in 3D. The line that passes through A and R can be written as:

r = a + λb
Vector equation of a line in 3D. Free online a-level further maths core pure 1 CP1 notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes.
  • where a is the position vector of a known point on the line

  • b is the direction vector of the line (a vector parallel to the line)

  • r is the position vector of any arbitrary point on the line

  • λ is a scalar parameter

If you need to find the equation of a line from just two points, C and D, and you do not know the direction vector, use the fact that the vector between the two points (d - c) is the direction vector of the line:

Vector equation of a line in 3D. Free online a-level further maths core pure 1 CP1 notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes.

The equation of this line is given as

r = c + λ(d-c)

Equations of 3D line in Cartesian Form

If you need to find the equation of a straight three dimensional line in Cartesian form (in terms of x, y and x), convert using the vectors a and b from the vector equation r = a + λb.

Cartesian equation of a line in 3D. Free online a-level further maths core pure 1 CP1 notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes.



Equations of a Plane in 3D

Vector equation of a plane in 3D. Free online a-level further maths core pure 1 CP1 notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes.