Basics of vectors - calculus, Mathematics

Assignment Help:

Vectors - The Basics

Let us start this section off with a quick discussion on what is the use of vector.  Vectors are utilized to present quantities that have both a magnitude and a direction.  Good instances of quantities that can be presented by vectors are force and velocity.  Both of these consist of a direction and a magnitude.  

 Let us consider force for a second.  A force of like 5 Newtons that is applied in a specific direction can be applied at any point in space.  Alternatively, the point where we apply the force does not alter the force itself.  Forces are not dependent of the point of application.  To describe a force all we need to know is the magnitude of the force and the direction which the force is applied in.

 Similar idea holds more usually with vectors.  Vectors just only impart magnitude and direction. 

They don't impart any type of information about where the quantity is applied.  This is an significant idea to all time remember in the study of vectors.

Graphically vectors are presented by directed line segments.  The direction of the line segment is the direction of the vector and length of the line segment is the magnitude of the vector.  Though, because vectors don't impart any information about where the quantity is applied any directed line segment along with similar length and direction will represent similar vector.

Consider the sketch below.  

1945_Basics of Vectors - Calculus 1.png

Every directed line segments in the sketch represents similar vector.  In each case the vector starts at a particular point after that moves 2 units to the left and 5 units up. The notation that we'll make use for this vector is,

1137_Basics of Vectors - Calculus 2.png

and each directed line segments in the diagram are called representations of the vector.


Related Discussions:- Basics of vectors - calculus

Kurtosis-measure of central tendency, Kurtosis - It is a concept, whic...

Kurtosis - It is a concept, which refers to the degree of peakedness of a described frequency distribution. The degree is generally measured along with reference to general di

Area related to circle, If ABCD isaa square of side 6 cm find area of shad...

If ABCD isaa square of side 6 cm find area of shaded region

Evaluate of the largest angle, The measures of the angles of a triangle are...

The measures of the angles of a triangle are in the ratio of 3:4:5. Evaluate of the largest angle. a. 75° b. 37.5° c. 45° d. 60° a. The addition of the measures of t

Mathematics Warm-Ups for CCSS, Ask question #Minimum 100 words accepted wha...

Ask question #Minimum 100 words accepted what is a ratio

Constructing a dfa/nfa or a regex), Let ∑ = (0, 1). Define the following la...

Let ∑ = (0, 1). Define the following language: L = {x | x contains an equal number of occurrences of 01 and 10} Either prove L is regular (by constructing a DFA/NFA or a rege

Exponential and logarithmic fuctions, How long does it take for an amount o...

How long does it take for an amount of money P to double itself if it is invested at 8% interest compounded 4 times a year?

Find out the minimum distance from the origin, Problem 1. Find the maximum...

Problem 1. Find the maximum and the minimum distance from the origin to the ellipse x 2 + xy + y 2 = 3. Hints: (i) Use x 2 + y 2 as your objective function; (ii) You c

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd