Perpendicular Vector with given magnitude

Click For Summary

Homework Help Overview

The problem involves finding vectors in the xy plane that are perpendicular to a given vector A = 8i − 5j and have a specified magnitude of 14.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to identify perpendicular vectors and is exploring how to adjust their magnitudes to equal 14. Some participants suggest using the properties of vector magnitudes and the dot product to find suitable vectors.

Discussion Status

Participants are actively discussing the relationship between the magnitude of vectors and their components. Some guidance has been offered regarding the use of multiples to achieve the desired magnitude, but confusion remains about how to apply this concept effectively.

Contextual Notes

There is an ongoing discussion about the nature of vector magnitudes and the possibility of using non-integer values to achieve the required magnitude of 14.

NEUhusky
Messages
5
Reaction score
0

Homework Statement



Given a vector A = 8i − 5j, find the vectors in the xy plane that are perpendicular to A and have a magnitude of 14.

The Attempt at a Solution



I can find the vector perpendicular to A quite easily. I'm having trouble finding the perpendicular line when it has the given magnitude of 14. I have a feeling it's going to be an easy solution but something isn't clicking in my brain at the moment. Any help would be greatly appreciated. Thanks!
 
Physics news on Phys.org
Welcome to PF!

Hi NEUhusky! Welcome to PF! :wink:

The magnitude of ai + bj is √(a2 + b2) …

show us what you get. :smile:​
 


tiny-tim said:
Hi NEUhusky! Welcome to PF! :wink:

The magnitude of ai + bj is √(a2 + b2) …

show us what you get. :smile:​

Thanks! Glad I found this place! :smile:

Hm, well the magnitude of the given vector A is √(8^2+5^2) which is approximately 9.43.

Using the dot product I know that the perpendicular lines are either B = -5i-8j or 5i+8j because the dot product equals zero. Unfortunately the magnitude is still the same as A when it needs to be 14. Still kinda lost.
 
ah!

no, 5i + 8j is a point on the perpendicular line …

multiply it by anything, and you'll get more points on the perpendicular line …

choose the correct multiples to get 14. :wink:
 
tiny-tim said:
ah!

no, 5i + 8j is a point on the perpendicular line …

multiply it by anything, and you'll get more points on the perpendicular line …

choose the correct multiples to get 14. :wink:

Ugh, still a bit confused. Multiples to get 14 would be either 2 & 7 or 1 & 14. I'm not sure how that applies. Doesn't the magnitude ( √(a2 + b2) ) have to equal 14?
 
Hi NEUhusky! :smile:

(just got up :zzz: …)
NEUhusky said:
Ugh, still a bit confused. Multiples to get 14 would be either 2 & 7 or 1 & 14. I'm not sure how that applies. Doesn't the magnitude ( √(a2 + b2) ) have to equal 14?

(try using the X2 icon just above the Reply box :wink:)

Yes, but it doesn't have to be an integer! :wink:
 

Similar threads

Perpendicular Unit Vectors in the x-y Plane: Is My Solution Correct?
  • · Replies 3 ·
Replies
3
Views
4K
Vector Subtract Given Magnitude
  • · Replies 6 ·
Replies
6
Views
2K
Perpendicular Component of Vector A in the Plane of A and B
  • · Replies 5 ·
Replies
5
Views
2K
Understanding Perpendicular Vector Components
  • · Replies 2 ·
Replies
2
Views
2K
Parallel and perpendicular vectors with given magnitude
  • · Replies 1 ·
Replies
1
Views
9K
Why Might a Rotating Ring in a B-field Ignore Certain Torques?
  • · Replies 2 ·
Replies
2
Views
2K
Things to talk about in a Polarization Write-up
  • · Replies 1 ·
Replies
1
Views
2K
How Do You Determine the Components of a Vector Perpendicular to Another?
  • · Replies 1 ·
Replies
1
Views
4K
Minimum and maximum resultant of three vectors.
  • · Replies 4 ·
Replies
4
Views
6K
A pair of perpendicular vectors
  • · Replies 3 ·
Replies
3
Views
7K