How Do You Calculate the Length of a Resultant Vector?

  • Thread starter Thread starter princiebebe57
  • Start date Start date
Click For Summary

Homework Help Overview

The discussion revolves around calculating the length of a resultant vector formed by the linear combination of two vectors, A and B, specifically in the context of vector operations in two-dimensional space.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the multiplication of vectors by scalar values and subsequent subtraction to find the resultant vector. There are questions regarding the correctness of intermediate results and the final calculation of the vector's magnitude.

Discussion Status

The discussion is active, with participants verifying calculations and exploring the steps necessary to find the magnitude of the resultant vector. Some guidance has been offered regarding the formula for vector magnitude, although participants express uncertainty at various points.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can share or the methods they can use. There is a focus on ensuring the correctness of each calculation step before proceeding.

princiebebe57
Messages
31
Reaction score
0
What is the length of the resultant vector of combining 2A - 3B where vector A= 4i + 3j and vector B= 9i + 8j?
 
Physics news on Phys.org
First thing is to multiply the vectors by the given amounts... post your result.
 
is it -19i + 30j?
 
princiebebe57 said:
is it -19i + 30j?
No, what's 2A and 3B?
 
2A = 8i + 6j
3B = 27i + 24j

is that correct?
 
princiebebe57 said:
2A = 8i + 6j
3B = 27i + 24j

is that correct?
Yep -- now do the subtraction.
 
so (8i + 6j)-(27i + 24j)?
 
princiebebe57 said:
so (8i + 6j)-(27i + 24j)?
Yeah. What's it equal?
 
is it -19i - 18j?
 
  • #10
princiebebe57 said:
is it -19i - 18j?
Yeah -- and the length (magnitude) is...
 
  • #11
i'm stuck at that!
 
  • #12
princiebebe57 said:
i'm stuck at that!

The magnitude of a vector x\vec{i}+y\vec{j}=\sqrt{x^2+y^2}. So, what does give you in your case?
 
Last edited:
  • #13
so is it 26.172?
 
  • #14
princiebebe57 said:
so is it 26.172?
Yep -- to 3 decimal places.
 
  • #15
Thank you so much!
 
  • #16
Hello princiebebe57,

you may find this website here interesting. It contains some questions and answers on vectors.
If you want to remember the formula for the length of a vector, it helps thinking of the Pythagorean theorem.
 

Similar threads

Magnitude, Unit vectors,unknown variables
  • · Replies 10 ·
Replies
10
Views
5K
Question about determining the angles of triangle given two vectors
  • · Replies 3 ·
Replies
3
Views
4K
Divergence of ##\vec{x}/\vert\vec{x}\vert^3##
  • · Replies 4 ·
Replies
4
Views
2K
How to show two lines intersect in a vector question.
  • · Replies 3 ·
Replies
3
Views
3K
Engineering Solving Problems Involving Complex Vectors
  • · Replies 2 ·
Replies
2
Views
1K
How can I prove that the dot product is distributive?
  • · Replies 1 ·
Replies
1
Views
2K
Finding the Basis Vectors for a Coordinate System
  • · Replies 6 ·
Replies
6
Views
4K
What is v×w if v, a, and b have length 1 and w has length 2?
  • · Replies 5 ·
Replies
5
Views
2K
Find the values of a and b to get max/min of certain expression
  • · Replies 21 ·
Replies
21
Views
3K
How Do Vector Spaces of Linear Maps Differ from Standard Vector Spaces?
  • · Replies 9 ·
Replies
9
Views
2K