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Mathematics · Ch 6 — Applications of Vector Algebra

Different Forms of Equation of a Straight Line

6.7.1

Different Forms of Equation of a Straight Line

A straight line is uniquely fixed by either of two kinds of data:

  • a point on the line, together with the direction of the line, or
  • two points on the line (the direction is then just the vector joining them).

To find the vector equation of a line, take an arbitrary point PP on the line with position vector r⃗\vec r, and use the given data (point-plus-direction, or two points) to write down a relation that r⃗\vec r must satisfy — that relation IS the vector equation of the line.

A vector equation may or may not carry a free real parameter:

  • if it involves a parameter (traditionally tt or ss), it is the equation in parametric form;
  • if no parameter appears, it is the equation in non-parametric form. …
Figure 6.18Fig. 6.18 - Vector equation of a straight line l through a point A with position vector a and parallel to vector b; a general point P has position vector r = a + t b.
Fig. 6.18 — Fig. 6.18 - Vector equation of a straight line l through a point A with position vector a and parallel to vector b; a general point P has position vector r = a + t b.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. Fig. 6.18 - Vector equation of a straight line l through a point A with position vector a and parallel to vector b; a general point P has position vect …

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