• Support PF! Buy your school textbooks, materials and every day products Here!

Vector with the same direction but a different magnitude

  • Thread starter Calpalned
  • Start date
  • #1
297
6

Homework Statement


Find a vector that has the same direction as <-2, 4, 2> but has length 6.

Homework Equations


Length of vector in 3D = |v| = (x2 + y2 + z2)0.5

The Attempt at a Solution


I can see that the length of the given vector is (-2)2 + 42 + 22 = 24
36 is (1.5)24, so I tried multiplying each component of the vector by the scalar 1.5. However, this doesn't give me the desired length of six (rather, it gives me the square root of 54). I had a feeling this method would be faulty, but nothing else comes to mind.
 

Answers and Replies

  • #2
11,519
5,069
Compare lengths not the squares of lengths to get the right factor.
 
  • #3
Fredrik
Staff Emeritus
Science Advisor
Gold Member
10,851
406
I can see that the length of the given vector is (-2)2 + 42 + 22 = 24
Not according to the formula you included under "relevant equations".
 
  • #4
297
6

Homework Statement


Find a vector that has the same direction as <-2, 4, 2> but has length 6.

Homework Equations


Length of vector in 3D = |v| = (x2 + y2 + z2)0.5

The Attempt at a Solution


I can see that the length of the given vector is (-2)2 + 42 + 22 = 24
36 is (1.5)24, so I tried multiplying each component of the vector by the scalar 1.5. However, this doesn't give me the desired length of six (rather, it gives me the square root of 54). I had a feeling this method would be faulty, but nothing else comes to mind.
I tried it again with the length of the desired vector = (F(-2)2 + F42 + F22)0.5 Where F = 1.5, and the answer seems to be correct...
 
  • #5
297
6
I just noticed my error. In my original attempt, (F * IJK)2 for each component I did when it should have been F(IJK2)
 
  • #6
33,314
5,006
I just noticed my error. In my original attempt, (F * IJK)2 for each component I did when it should have been F(IJK2)
Perhaps you understand what you mean, but this is very weird notation. If u = <a, b, c> and v = 2<a, b, c>, then |v| = 2|u|
 

Related Threads on Vector with the same direction but a different magnitude

  • Last Post
Replies
1
Views
5K
Replies
0
Views
2K
Replies
3
Views
1K
Replies
4
Views
9K
Replies
0
Views
903
Replies
2
Views
2K
Replies
8
Views
1K
  • Last Post
Replies
3
Views
1K
Replies
4
Views
2K
Replies
2
Views
2K
Top