Question

prove this formula

Answer 1

\[R = \sqrt{|a ^{2}| + |b ^{2}| + |a||b|\cos \theta}\]

Answer 2

and this formula:

Answer 3

\[R = \sqrt{|a ^{2}|+|b ^{2}| - |a||b|\cos \theta} \]

Answer 4

what are these formulas in reference to?
given the constants a,b,theta ... the 2 formulas seem to contradict each other if "R" is same in each

Answer 5

To prove these you need to use the Parallelogram Law of Vector addition where you get the magnitude resultant vector(R) of the 2 vectors A and B inclined at angle theta.
Understood? :)

Answer 6

@dumbcow , these formulas are used about "Vectors".
@AkashdeepDeb , No I didn't understand! can you prove or explain it more?

Answer 7

Yes, hold on a sec.

Answer 8

Thank you :)

Answer 9

you have that R equals two different things.

Answer 10

And for proving R equals the second one just take a the vectors with the same magnitude but one vector in the opposite direction! :)
Understood? :)

Answer 11

@AkashdeepDeb , Thank you,Thank you!I understood it!!!
@zzr0ck3r , NO!This is two different formula!

Answer 12

:)