Resultant of two vectors of equal magnitude

[gracy]

Homework Statement

Resultant of two vectors of equal magnitude A is
a) √3 A at 60
b) √2 A at 90
c) 2A at 120
d) A at 180

Homework Equations

When two vectors are of equal magnitudes then their resultant is
$A_R$ = 2 A Cos θ/2

The Attempt at a Solution

I think we need more information especially the angle between the given two vectors . Or we can eliminate options one by one. Answer is both a & b
I tried to cross check it . If the resultant is at 60 it means angle between the vectors we started with is 120 i.e θ =120
if we plug in the numbers
$A_R$ = 2A Cos 120/2
= 2A cos 60
= 2A 1/2
= A
which is not equal to √3
Similarly for option b
$A_R$ = 2A Cos 180/2
= 2A cos 90
= 2A 0
= 0
I 'll get it correct if I directly put θ=60 & 90 respectively . But as far as I know θ in this formula $A_R$ = 2 A Cos θ/2 is angle between the two vectors and not the vector and resultant

 

[cnh1995]

I think we need more information especially the angle between the given two vectors

Right. The question doesn't make sense.

 

[TomHart]

I think you are right - that the angles shown in the problem statement are the original angles between the 2 vectors of magnitude A.

 

[Student100]

Homework Statement

Resultant of two vectors of equal magnitude A is
a) √3 A at 60
b) √2 A at 90
c) 2A at 120
d) A at 180

Homework Equations

When two vectors are of equal magnitudes then their resultant is
$A_R$ = 2 A Cos θ/2

The Attempt at a Solution

I think we need more information especially the angle between the given two vectors . Or we can eliminate options one by one. Answer is both a & b
I tried to cross check it . If the resultant is at 60 it means angle between the vectors we started with is 120 i.e θ =120
if we plug in the numbers
$A_R$ = 2A Cos 120/2
= 2A cos 60
= 2A 1/2
= A
which is not equal to √3
Similarly for option b
$A_R$ = 2A Cos 180/2
= 2A cos 90
= 2A 0
= 0
I 'll get it correct if I directly put θ=60 & 90 respectively . But as far as I know θ in this formula $A_R$ = 2 A Cos θ/2 is angle between the two vectors and not the vector and resultant

I don't see the problem, it seems to me it's giving you the angles between the two vectors to check and what the resultant magnitude should be, so A and B are both correct as you say.