True or False: Magnitude (v+v) = 2*Magnitude (v)

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In summary, the conversation discusses a true or false question about the magnitude of a vector. The OP solved the problem using a previous experience and others confirmed that the answer was indeed correct. The conversation also includes some humor about reading carefully and the concept of a vector being perpendicular to itself.
  • #1
Mdhiggenz
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Homework Statement



So I took my calc 3 exam today and had this question

true or false

magnitude ( v+v) = 2*magnitude( v)

I put true.

Thoughts?


Homework Equations





The Attempt at a Solution

 
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  • #2
You got it correct. Were you just guessing?
 
  • #3
No I did a problem where I had to solve for K in the magnitude give the value of v. Pretty much I took k from the magnitude and solved for it. So I was hoping the same thing applied here.
 
  • #4
LCKurtz said:
You got it correct.
Really? I don't see how this is correct.
 
  • #5
oay said:
Really? I don't see how this is correct.

If ##\vec v = \langle a,b,c\rangle## what do you get for ##|\vec v|## and ##|2\vec v|##?
 
  • #6
LCKurtz said:
If ##\vec v = \langle a,b,c\rangle## what do you get for ##|\vec v|## and ##|2\vec v|##?
Sorry, of course it's correct.

I was having a senile moment when I was imagining the two vectors weren't the same! D'oh! :redface:
 
  • #7
oay said:
Sorry, of course it's correct.

I was having a senile moment when I was imagining the two vectors weren't the same! D'oh! :redface:

Don't feel to bad about that. My first reaction was the same because I was expecting the question to read u+v since, in my opinion, that would have been a better question. Only after I started my reply did I realize the OP had v+v.
 
  • #8
oay said:
Sorry, of course it's correct.

I was having a senile moment when I was imagining the two vectors weren't the same! D'oh! :redface:
Did the same thing here. :smile:
 
  • #9
LCKurtz said:
Don't feel to bad about that. My first reaction was the same because I was expecting the question to read u+v since, in my opinion, that would have been a better question. Only after I started my reply did I realize the OP had v+v.
vela said:
Did the same thing here. :smile:

I obviously need to learn to read twice before posting. Something which you two are obviously better at than me! :smile:
 
  • #10
If v happened to be perpendicular to itself, the original statement wouldn't be true.:-p

(The zero vector not included, of course.)
 
  • #11
Mark44 said:
If v happened to be perpendicular to itself, the original statement wouldn't be true.:-p

(The zero vector not included, of course.)

Now you've lost me!
 
  • #12
Math humor...

A nonzero vector can't be perpendicular to itself.
 
  • #13
Mark44 said:
Math humor...

A nonzero vector can't be perpendicular to itself.

What if it's bent?
 

Related to True or False: Magnitude (v+v) = 2*Magnitude (v)

1. Is the statement "Magnitude (v+v) = 2*Magnitude (v)" always true?

No, the statement is not always true. It depends on the vector v. If v has a magnitude of 0, then the statement will be true. However, if v has a non-zero magnitude, the statement will be false.

2. Can the magnitude of a vector be negative?

No, the magnitude of a vector is always a positive value. It represents the size or length of the vector in a given direction.

3. Is the magnitude of a vector affected by its direction?

Yes, the magnitude of a vector is affected by its direction. Two vectors with the same magnitude but different directions will have different results when added together.

4. Can the magnitude of a vector be greater than the sum of its components?

Yes, the magnitude of a vector can be greater than the sum of its components. This is because the magnitude takes into account both the magnitude and direction of the vector, whereas the sum of components only considers the numerical values.

5. How is the magnitude of a vector calculated?

The magnitude of a vector is calculated by taking the square root of the sum of the squared components. This can be represented by the formula ||v|| = √(v12 + v22 + ... + vn2), where v is the vector with n components.

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