Resultant of two orthogonal vectors

[Crystal037]

Homework Statement

The resultant of two orthogonal vectors makes an angle θ with their difference. if magnitude of one is 2 times that of the other, find the value of sec θ.

Relevant Equations

|a+b|=sqrt(a^2 +b^2 +2ab)

But the answer in my book is given that sec(theta) =3. Where am I going wrong?

 

[BvU]

Where am I going wrong?

I think nowhere. So the book answer must be a mistake.
You could come up with a better drawing, though. And a sign of the secant is minus if b = 2a.

 

[Crystal037]

Maybe I am interpreting the question wrongly. I don't know if that is what the question is supposed to mean.

 

[BvU]

You worked out your interpretation. You think there is an alternative ?

 

[SammyS]

Homework Statement:: The resultant of two orthogonal vectors makes an angle θ with their difference. if magnitude of one is 2 times that of the other, find the value of sec θ.
Relevant Equations:: |a+b|=sqrt(a^2 +b^2 +2ab)

Your relevant equation is wrong, unless by ab, you mean the scalar product of vector a and vector b .

As far as a different reading of the problem (Yes, the given statement is ambiguous.):

Rather than one and the other referring to the two orthogonal vectors, perhaps they refer to the resultant and the difference vectors. Is this even possible?

 

[BvU]

Is this even possible?

If two vectors $\vec a$ and $\vec b$ are orthogonal, then $\vec a\cdot\vec b=0 \Rightarrow |\vec a + \vec b | = |\vec a - \vec b |$

 

[kuruman]

Stated differently, if the vectors are orthogonal, one can form a $a\times2a$ rectangle with them. One diagonal is the sum, the other is the difference and they have equal magnitudes. There are two angles between the diagonals to be considered, one being the supplementary of the other.

 

[vela]

One comment about your notation: when the problem says "the magnitude of one is 2 times that of the other", it's not correct to write $\vec b = 2 \vec a$. That would imply that the two vectors are parallel to each other and not orthogonal.

 

[SammyS]

If magnitude of one is 2 times that of the other, find the value of sec θ.

Try this instead.

If magnitude of one is $\sqrt{2~}$ times that of the other, find the value of sec θ.

 

[Crystal037]

Try this instead.

If magnitude of one is $\sqrt{2~}$ times that of the other, find the value of sec θ.

Yes then the answer comes as 3.