Vector (Line in Space), Summaries of Engineering Mathematics

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Engineering Mathematics 1

Lines

In Space

VECTOR

A line in space is the set of terminal points of vectors emanating from a given point that are parallel to a fixed vector, v. The fixed vector in the definition is called a direction vector for the line. a) The Equations of Lines in Space :

• Parametric Equation.
• Symmetric Equation. b) Angle between Two Lines. c} Intersection of Two Lines. d) Shortest Distance from a Point to a Line.

What is Lines in Space?

Vector equations of a line can be computed with the help of any two points on the line, or with the help of a point on the line and a parallel vector. The two methods of forming a vector form of the equation of a line are as follows. Vector Equations of a Lines Vector Equations :

The parametric equations for the line through P (xο, yο, zο) parallel to v = ai + bi + ck are Parametric Equations for a Lines Parametric Equations :

The cosine of the angle between two vectors can be calculated by dividing the dot product of the vectors by-product of their magnitudes. Angle between Two Lines

Intersection of Two Lines When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. Two vectors in space will either be parallel, intersecting or skew