Q .4. Provide two sets of geometric co... [FREE SOLUTION]

Chapter 10: Q .4. (page 833)

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

Short Answer

Expert verified

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 by step solution

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 $3 d -$ 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 $3 d -$ space.

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

For the point } $(x_{0}, y_{0}, z_{0})$ and the direction vector } $(a, b, c)$ the line equation is as follows,

$r (t) = (x_{0}, y_{0}, z_{0}) + t (a, b, c)$

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91影视

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

Short Answer

Step by step solution

Step 1:Given information

Step 2:Explaination

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