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In the formula for the mag of the resultant of the difference of 2 vectors
sq root(a^2 + b^2 - 2abcos$)
is $ the angle between a and b or between a and -b?
$ is the angle between A and -B orr.. B and -A
it is the angle between a and -b.
as we know,
we know that a+b=sq.root(a2+b2+2abcosA)
where A is the angle between a and b.
here he asked the difference so we shoud replace b with -b.
then,a-b=sq.root(a2+b2+2a(-b)cosA)
threfore here A=angle between a and-b.
Hi Shayan,
Analyse the problem and try to simplify it,
The question says mag of resultant of 2 Vectors = |a - b|
Now |a-b|2 = (a-b).(a-b) = |a|2+|b|2 - 2a.b
or |a-b| = (|a|2+|b|2 - 2a.b)1/2.
So $ is certainly the angle between vector "a" and vector "b".
Regards,
Ashwin (IIT Madras).
Shayan,
If in the expression you had
(a^2 + b^2 + 2(a)(-b)cos$), then it would have been the angle between a and -b.
These kinds of traps are generally set by IITs in the exam, and one needs to be carefule.
In this case it is the angle between a and b only.
Sorry for being stupid but I really didnt get any of this...
Plz explain again
No worries.
The question requires one to find if "$" is the angle between "a" & "b" or "a" & "-b"
So you have to compare the final result with the given expression in the question.
You have |a-b| = sqrt{ a^2 + b^2 - 2a.b} as in the above working.
Compare this with the expression in your question.
we will have a.b = ab(cos$)
which shows that $ is the abgle between "a" vector and "b" vector.
Hope this helps.
Best Regards,
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