Physics, Chemistry, Mathematics Forums

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i have a doubt here..
the question is:
if [a vector+3(b vector)] is perpendicular to [7(a vector)-5(b vector)] and [a vector-5(b vector)] is perpendicular to [7(a vector)+3(b vector)].find the angle between a vector and b vector.
This problem is a simple one and on solving one can readily obtain the solution as the angle to be 90 degrees.
But considering the first and second equations of the two perpendicular vector cases,you may find that arbitary values of a and b do not necessarily satisfy the equations.In that cases there is a contradiction of the vectors not being perpendicular.How is that possible?
I hope you have understood my question.If not,please solve the question by expanding using scalar product and you will know where the fault lies.

Clausius clapeyron equation, logP=-A/T +B shows that vapour pressure increases as temperature increases.Is this also valid for gases ?

Which of the following azeotropic solutions has boiling point less than the boiling point of its constituent A and B-CHLOROFORM and PROPANOIC ACID; CARBON SULPHIDE and PROPANOIC ACID; ETHYL ALCOHOL and CHOROFORM: ETHANAL and CARBON SULPHIDE.

find the integral of :

(sec x . dx)/{ sin(2x+A) + sin A}^1/2

a) secA. {tanx.sinA +cosA)^1/2 + K       (K-constant here)

b)2^1/2 .sec A {tanA +sinAcosA)^1/2 + K

c) 2^-1/2.secA (tanA.sinA + cos A)^3/2 + K

d) none of these

Q. Which of the following will give a white ppt. when refluxed with ethanolic silver nitrate in conc. HNO₃???
(a) Benzyl Chloride
(b) CH₃CH₂CH₂NH₂⁺Cl^-
(c) Phenyl Chloride
(d)None

It was a multiple correct ques. What should be the answer? I have doubt in only a or both a nd b. Plz reply soon

Imagine a solid metal cube moving in the positive y direction at a constant velocity v and it moves through a uniform magnetic field B directed towards the positive z direction.Which cube face is at a lower potential and which is at a higher  potential?

While solving problems, I have seen that the work done in reversible process comes out to be greater than that in irreversible process.

How can it be explained theoretically?

Please answer my doubt.

Is there any general formula for 1^x + 2^x + 3^x ...... + n^x ??

prove that x²+4y²+16z²-2xy-8yz-4zx=0 represents a line passing through the origin!

I had 2 small doubts.

Will a current loop placed in a magnetic field always experience a zero force?

The net charge in a current carrying wire is zero.Then why does a magnetic field exert a force on it?