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Squaring of vectors in absolute value

by M. next
Tags: absolute, squaring, vectors
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M. next
#1
Sep26-13, 02:09 PM
P: 378
Is |[itex]\vec{a}[/itex]+[itex]\vec{b}[/itex]|[itex]^{2}[/itex] equal to the same thing as ([itex]\vec{a}[/itex]+[itex]\vec{b}[/itex])[itex]^{2}[/itex]? And when is it equal to √(a[itex]^{2}[/itex]+b[itex]^{2}[/itex])?

Thanks.
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Mark44
#2
Sep26-13, 02:45 PM
Mentor
P: 21,286
Quote Quote by M. next View Post
Is |[itex]\vec{a}[/itex]+[itex]\vec{b}[/itex]|[itex]^{2}[/itex] equal to the same thing as ([itex]\vec{a}[/itex]+[itex]\vec{b}[/itex])[itex]^{2}[/itex]?
They're the same, assuming the implied multiplication in the expression on the right is the dot product. Otherwise, multiplication of one vector by another is not defined (with the exception of the cross product).
Quote Quote by M. next View Post
And when is it equal to √(a[itex]^{2}[/itex]+b[itex]^{2}[/itex])?
Tip: You don't need so many tex or itex tags. Your squared vector sum can be written like this:
[itex](\vec{a} +\vec{b})^2 [/itex]
Or instead of the itex tags, you can use ## delimiters at the front and back.
M. next
#3
Sep27-13, 12:40 AM
P: 378
Thank you for the reply and the tip. But about the √(a^2+b^2)?? My second part of the question?

Astrometry
#4
Sep27-13, 01:41 AM
P: 32
Squaring of vectors in absolute value

Quote Quote by M. next View Post
Thank you for the reply and the tip. But about the √(a^2+b^2)?? My second part of the question?
That is merely the magnitude of both vectors. Assuming that's what you mean? You were a little unclear on the second part. Think of magnitude as the size or length of those two vectors.
Tanya Sharma
#5
Sep27-13, 02:08 AM
P: 1,315
Quote Quote by M. next View Post
Thank you for the reply and the tip. But about the √(a^2+b^2)?? My second part of the question?
[itex]\sqrt{a^2+b^2}[/itex] is the magnitude of [itex]\vec{a}\vec{b} [/itex],where [itex]\vec{a}[/itex] and [itex]\vec{b}[/itex] are orthogonal (perpendicular) vectors.
M. next
#6
Sep27-13, 02:09 AM
P: 378
Okay. Thank you, yes, it is exactly what I meant.


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