PURE MATHEMATICS - Vectors

 

Vector Equations

 

 

Component Rules

Equation - Single Point & Parallel Vector

Equation - Two Points

 

 

 

Component Rules

 

Consider two vectors in three dimensional space.

 

 

 

Where 'm' is a scalar quantity.

 

 

Hence, the magnitudes of a and b are given by:

 

 

 

 

 

In 3D space, if point A has position vector a and point B has position vector b then the distance AB is given by:

 

 

 

 

back to top

 

 

Equation of a Straight Line - single point & parallel vector given

 

 

vector equation from one point and a parallel vector

 

 

A(x1 y1 z1) is a fixed point on the line.

 

a is the position vector for point A   a = x1i + y1 j+ z1k

 

s is a vector parallel to the line   s = l i + m j+ n k


(l m n are called the direction ratios of the line)

 

r is the position vector for an arbitrary point P(x, y, z) on the line.

 

 

vector equations #1

 

 

back to top

 

 

Equation of a Straight Line - two points given

 

 

vector equation from two points on a line

 

 

A(x1 y1 z1) is a fixed point on the line

 

a is the position vector for point A   a = x1i + y1 j+ z1k

 

B(x2 y2 z2) is a fixed point on the line

 

b is the position vector for point B   b = x2i + y2 j+ z2k

 

r is the position vector for an arbitrary point P(x, y, z) on the line.

 

 

vector equations#2

 

 

 

 

 

back to top

 

 

 

this week's promoted video

 

 from Physics Trek

 

 

creative commons license

All downloads are covered by a Creative Commons License.
These are free to download and to share with others provided credit is shown.
Files cannot be altered in any way.
Under no circumstances is content to be used for commercial gain.

 

 

 

 

©copyright a-levelmathstutor.com 2020 - All Rights Reserved