Vectors
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Vectors and Coordinate Systems, Lecture notes of Civil Engineering
An overview of vector quantities, including their mathematical operations such as addition and subtraction. It introduces the cartesian and polar coordinate systems, which are used to describe the position of a point in space. The document also discusses the differences between scalar and vector quantities, and explains the methods for adding vectors, including graphical and algebraic approaches. Additionally, it covers the concept of unit vectors and how they are used to specify direction. The document could be useful for students studying physics, mathematics, or engineering, as it covers fundamental concepts related to vectors and coordinate systems that are essential in these fields.
Typology: Lecture notes
2022/2023
1 / 40
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Vectors and Coordinate Systems and more Lecture notes Civil Engineering in PDF only on Docsity!
Vectors
Vectors Vector quantities
- (^) Physical quantities that have both numerical and directional properties
- (^) Mathematical operations of vectors
- Addition
- (^) Subtraction
Cartesian Coordinate System Also called rectangular coordinate system x- and y- axes intersect at the origin -Points are labeled (x,y)
- (^) Polar Coordinate System Origin and reference line are noted Point is distance r from the origin in the direction of angle , ccw from reference line
- (^) The reference line is often the x-axis.
- (^) Points are labeled (r, )
Example
Vectors and Scalars
A scalar quantity is completely specified by a single value with an appropriate unit and has no direction.
- (^) Many are always positive
- (^) Some may be positive or negative
- (^) Rules for ordinary arithmetic are used to manipulate scalar quantities. A vector quantity is completely described by a number and appropriate units plus a direction.
When adding vectors, all of the vectors must have the same units. All of the vectors must be of the same type of quantity.
- (^) For example, you cannot add a displacement to a velocity.
Multiplying or Dividing a Vector by a Scalar
- (^) The result of the multiplication or division of a vector by a scalar is a vector.
- (^) The magnitude of the vector is multiplied or divided by the scalar.
- (^) If the scalar is positive, the direction of the result is the same as of the original vector.
- (^) If the scalar is negative, the direction of the result is opposite that of the original vector.