Question

write a parametric vector equation and a system of parametric Cartesian equations for the line containing the given points $S$ and $T$. $\mathbf{S}(3,2), \mathbf{T}(1,1)$

   write a parametric vector equation and a system of parametric Cartesian equations for the line containing the given points $S$ and $T$.
$\mathbf{S}(3,2), \mathbf{T}(1,1)$

Modern Analytic Geometry

William Wooton,… 1st Edition

Chapter 2, Problem 2

Instant Answer

Step 1

The coordinates are given as $ \mathbf{S}(3, 2) $ and $ \mathbf{T}(1, 1) $. Show more…

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write a parametric vector equation and a system of parametric Cartesian equations for the line containing the given points $S$ and $T$. $\mathbf{S}(3,2), \mathbf{T}(1,1)$

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Key Concepts

Direction Vector

The direction vector determines the orientation of a line and can be obtained by subtracting the coordinates of two distinct points on the line. It plays a crucial role in both vector and parametric representations, as it defines the line's slope and direction in space.

Vector Equation of a Line

A vector equation expresses a line in terms of a fixed position vector (representing a specific point on the line) plus a scalar multiple of a direction vector. This form encapsulates both the location and the direction of the line in a concise mathematical statement, making it useful for many applications in geometry and physics.

Parametric Equations

Parametric equations represent the coordinates of the points on a line as functions of a common parameter. This approach translates the geometric concept of a line into algebraic expressions that describe the motion along the line as the parameter varies.

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