Position and Displacement Vectors in Mathematics
LO: Identify position vectors.
3 March 2025
Position vectors
Position vectors
Example:
(7, 4)
The point P
with coordinates (7, 4)
has position
vector:
=
P
=7
i
+ 4
j
=
=
x
i
+
y
j
The point P with coordinates (x, y) has position vector
(x, y)
Displacement vectors
Consider the points A(4, 5) and
B(8, 4)
From this diagram we can
see that
and
Thus we could write
A
B
We can describe this
movement as going directly
from A to B
Or we describe this movement using the position vectors
The vector is called the resultant of the vectors
and
Recall that
Example 1
Points A and B have coordinates (-4, 3, 0) and (-3, 6, 4)
respectively.
Find the vector
First we write the position vector
and
=
=
–
Resultant vectors
Similarly if we know a vector and a vector then each
of the points Q and R are given relative to point P.
We can write:
R
P
Q
=
+
=
–
Example 2
Given that
=
=
–
Find the vector
Example 3
Show that the points A, B and C with position vectors
i
– 2
j
+
3
k,
– 2
i
+ 3
j
–
k
and 4
i
– 7
j
+
7
k
respectively are
collinear
=
=
–
Find the vector
=
=
–
Find the vector
Thank you for using resources from
https://www.mathssupport.org
If you have a special request, drop us an email
info@mathssupport.org
For more resources visit our website
Learn about position vectors, displacement vectors, resultant vectors, and collinearity of points in mathematics. Explore examples and understand how to find vectors and determine relationships between points using vector operations.
Uploaded on Mar 03, 2025 | 0 Views
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
3 March 2025 Position vectors LO: Identify position vectors. www.mathssupport.org www.mathssupport.org
Position vectors Position vectors are vectors giving the position of a point, relative to a fixed origin, O. The point P with coordinates (7, 4) has position vector: Example: 5 (7, 4) (x, y) P 4 7 4 3 =7i + 4j OP = 2 1 0 6 7 8 5 1 2 3 O 4 The point P with coordinates (x, y) has position vector x y =xi + yj OP = www.mathssupport.org www.mathssupport.org
Displacement vectors Consider the points A(4, 5) and B(8, 4) From this diagram we can see that 4 1 We can describe this movement as going directly from A to B Or we describe this movement using the position vectors 6 A 5 B 4 = AB 3 2 1 0 6 7 8 5 1 2 3 O 4 9 10 OA and OB Thus we could write The vector is called the resultant of the vectors AB OA and OB Recall that AO = OA AB = AO + OB AB = OB OA www.mathssupport.org www.mathssupport.org
Example 1 Points A and B have coordinates (-4, 3, 0) and (-3, 6, 4) respectively. Find the vector First we write the position vector AB OA and OB -3 6 4 -4 3 0 OA = OB = 1 3 4 -3 6 4 -4 3 0 OB - OA AB = = = www.mathssupport.org www.mathssupport.org
Resultant vectors Similarly if we know a vector and a vector then each of the points Q and R are given relative to point P. PR PQ P R Q We can write: = PR + QR QP = PQ PR www.mathssupport.org www.mathssupport.org
Example 2 Given that 0 2 1 -8 -2 XY = XZ = -3 Find the vector YZ -2 -9 1 0 2 1 -3 -8 -2 XZ - XY YZ = = = www.mathssupport.org www.mathssupport.org
Example 3 Show that the points A, B and C with position vectors i 2j + 3k, 2i + 3j k and 4i 7j + 7k respectively are collinear 1 -2 3 Find the vector -2 3 -1 4 -7 7 OA = OB = OC = AB -3 5 -4 -2 3 -1 1 -2 3 OB- OA AB = = = Find the vector AC AB = AC 3 4 -7 7 1 -5 4 -2 3 OC- OA AC = = = www.mathssupport.org www.mathssupport.org
Thank you for using resources from A close up of a cage Description automatically generated For more resources visit our website https://www.mathssupport.org If you have a special request, drop us an email info@mathssupport.org www.mathssupport.org www.mathssupport.org
