What Must Be the Angle Between Two Vectors of Equal Magnitude?

[madinsane]

Homework Statement

Two vectors A and B have precisely equal magnitudes. In order for the magnitude of A+B to be 120 times larger than the magnitude of A-B , what must be the angle between them?

Homework Equations

None (i think)

The Attempt at a Solution

A+B=120(A-B)
(xi+yi)+(xi+yi)
2x+2y=120(2x+2y)
2x+2y+240x-240y
Then I don't know where to go from here
Is what I am doing even correct?
Point me in the right direction

 

[jedishrfu]

Have you learned about the vector inner or dot product? Look at its definition and usage.

 

[madinsane]

Have you learned about the vector inner or dot product? Look at its definition and usage.

No, please explain further

 

[drawar]

Draw a right-angled triangle ABC where BC is the hypotenuse, O is the midpoint of BC. You wil see that one of the two other sides is the magnitude of the vector-sum and the other is the magnitude of the vector-difference. A bit of trigonometry would lead you to the answer.

 

[madinsane]

Draw a right-angled triangle ABC where BC is the hypotenuse, O is the midpoint of BC. You wil see that one of the two other sides is the magnitude of the vector-sum and the other is the magnitude of the vector-difference. A bit of trigonometry would lead you to the answer.

Could you please expand?
Like what is the significance of knowing O?,etc

 

[gneill]

Homework Statement

Two vectors A and B have precisely equal magnitudes. In order for the magnitude of A+B to be 120 times larger than the magnitude of A-B , what must be the angle between them?

Homework Equations

None (i think)

The Attempt at a Solution

A+B=120(A-B)
(xi+yi)+(xi+yi)
2x+2y=120(2x+2y)
2x+2y+240x-240y
Then I don't know where to go from here
Is what I am doing even correct?
Point me in the right direction

You're free to choose whatever coordinate system and initial vector length you want to solve the problem. I might suggest that you choose a unit vector length and place your coordinate system so that one of the vectors lies along one of the coordinate axes. Then the other vector makes angle θ with that axis.

 

[drawar]

 

[madinsane]

yeah, but how is that helpful/relevant?

 

[drawar]

Then the angle between vectors a and b is two times the angle between BC and AB, which should be calculated using tangent formula.

 

[madinsane]

Then the angle between vectors a and b is two times the angle between BC and AB, which should be calculated using tangent formula.

Okay, I am starting to understand.
so if we name the angle between AB and BC as θ, then we can get it by,
Tan^-1(a-b/a+b)
then we multiply the result by 2
but then... we don't have a and b
all we know is that lAl=lBl
How can that help us get a and b?
Thank you so much btw...you're helping me h=get closer to the answer

 

[madinsane]

You're free to choose whatever coordinate system and initial vector length you want to solve the problem. I might suggest that you choose a unit vector length and place your coordinate system so that one of the vectors lies along one of the coordinate axes. Then the other vector makes angle θ with that axis.

I don't know what you mean?
can you expand

 

[gneill]

You're free to choose whatever coordinate system and initial vector length you want to solve the problem. I might suggest that you choose a unit vector length and place your coordinate system so that one of the vectors lies along one of the coordinate axes. Then the other vector makes angle θ with that axis.

I don't know what you mean?
can you expand

If vector A is a unit vector and lies along the x-axis, then its vector components are (1,0). If vector B makes some angle θ with A, then its vector components must be (cos(θ),sin(θ)). You can thus form A + B and A - B algebraically from those components. Write expressions for the magnitude of each and apply your required relationship between them.

 

[drawar]

But the magnitude of the vector-sum is 120 times that of the vector-difference. The tangent formula only requires a RATIO between two sides of the triangle.