two vector having equal magnitude A makes an angle "theta" with each other. find the magnitude and direction of the resultant.

Asked by riya sinha | 15th Jun, 2013, 08:01: AM

Expert Answer:

Pick the x axis as half way between the two. Call them A and B, with A below the x axis by ?/2 and B above by ?/2

Use normal vector arithmetic, get the x and y components of each

Ax = Acos(?/2)
Ay = –Asin(?/2)
Bx = Acos(?/2)
By = Asin(?/2)

add the components to get the components of the resultant

Rx = 2Acos(?/2)
Ry = 0

combine the components to get magnitude and angle.
with one zero, it is just the other component.

R = ?(Rx² + Ry²)
R = 2Acos(?/2)

angle = tan^-1[ (Ry/Rx) ]
With Ry=0, that becomes 0
Angle = 0

Angle will be halfway between the two. 

Answered by  | 15th Jun, 2013, 05:13: PM

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