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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
• 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:

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.