Q .4. - Calculus

Question

Provide two sets of geometric conditions that can be used to determine a line. 

Step-by-Step Solution

Answer

To write the equation of a line in three - dimensional space we need a point on the line and a parallel vector on the line.

Step 1:Given information

Geometric conditions that can be used to determine a line 

Step 2:Explaination

A line in a plane can be determined by two distinct points or a single point and a direction, specified by a vector.

In $3d-$ space lines cannot be described by a single linear equation, they are described by parametric equations.

A direction vector, which designates the direction of the line, and a point that passes through, we can obtain the equation of a line in a$3d-$ space.

To write the equation of a line in $3d-$space we need a point on the line and a parallel vector on the line.

 For the point }$\left(x_0,y_0,z_0\right)$ and the direction vector }$(a, b, c)$ the line equation is as follows, 

$r\left(t\right)=\left(x_0,y_0,z_0\right)+t(a,b,c)$