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06Representation of a Line in the Plane

# 06Representation of a Line in the Plane - REPRESENTATION OF...

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R EPRESENTATION OF A L INE IN THE P LANE When describing a line in two dimensions we are used to Cartesian form. This form gives a direct relation between x and y. However, there are other different ways of describing a line in two or three dimensions. Cartesian form (in 2D) – coordinates of a point on the line and the slope of the line Vector form – position vector of a point on the line and a vector parallel to the line (note: this is also sometimes called parametric form) Consider a line which passes through point A and is parallel to vector b . b R A To find the vector equation of this line, r , consider a general point R on the line. Let R have position vector r. R A is parallel to b , therefore b t R A = , but r a R A + - = . Therefore, b t r a = + - and b t a r + = . The vector form of a line is d t p r + = , where p is any point on the line, d is any vector in the direction of the line, and t is any value. The parametric form is +

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06Representation of a Line in the Plane - REPRESENTATION OF...

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