Question

the vector sum of two forces is perpendicular to their vector difference.in that case,the force is
a. are equal to eachother
b.are equal to eachother in magnitude
c. are not equal to each other in magnitude
d.can not be predicted

Answer 1

ooooo I know this one

Answer 2

I think it is c or b but I am not sure

Answer 3

I think it's B

Answer 4

ya its b but how

Answer 5

thank you ilove cake and freewilly :)

Answer 6

but may i know how?

Answer 7

Okay....... Here is a link: http://mathworld.wolfram.com/VectorSum.html

Answer 8

Does that help?

Answer 9

ilovecake.....no it doesnt..i want answer to this question specifically....thanx anyways

Answer 10

Let \(A = a_1i+a_2j\) and \(B = b_1i+b_2j\). Then,

\(A+B = (a_1+b_1)i+(a_2+b_2)j\) ; \(A-B = (a_1-b_1)i+(a_2-b_2)j\)

"the vector sum of two forces is perpendicular to their vector difference"
Therefore, their dot product must be zero.
\((A+B).(A-B) = (a_1+b_1)(a_1-b_1)+(a_2+b_2)(a_2-b_2) = \\
a_1^2-b_1^2+a_2^2 - b_2^2 = (a_1^2+a_2)^2-(b_1^2+b_2^2) = 0 \\
(a_1^2+a_2^2) = (b_1^2+b_2^2) \\
\sqrt{(a_1^2+a_2^2)} = \sqrt{(b_1^2+b_2^2)} \\
|A| = |B|
\)

Answer 11

thanx aum