Describe vectors?

Two vectors V1 and V2 add to a resultant:





V = V1 + V2





Describe V1 and V2 if


a) V =V1+ V2


b) V^2 = V1^2 + V2^2


c) V1 + V2 = V1 - V2





This is a question from chapter 3 of a physics textbook. Please help, I will be sure to rate you A++, thank you!!

Describe vectors?
let us take angle (p) between 2 vectors V1 %26amp; V2, and their resultant as V


we have resultant


V^2 = V1^2 + V1^2 + 2 V1 V2 cos (p) ----- (1)


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a) V =V1+ V2 put in (1)


V^2 = V1^2 + V1^2 + 2 V1 V2 cos (p)


(V1+V2)^2 = V1^2 + V1^2 + 2 V1 V2 cos (p)


2 V1 V2 = 2 V1 V2 cos (p)


cos (p) = 1


p = 0 degree so in (a) 2 vectors will be parallel vectors


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b) V1^2 + V2^2 = V1^2 + V1^2 + 2 V1 V2 cos (p)


2 V1 V2 cos (p) = 0


cos (p) = 0


p = pi/2 = 90 degree so in (b) 2 vectors will be perpendicular or normal vectors


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c) V1 + V2 = V1 - V2


it gives an impression that v2=0 = null vector, lets see


squaring both sides


V1^2 + V1^2 + 2 V1 V2= V1^2 + V1^2 - 2 V1 V2


4 V1 V2 =0


V1 V2 =0


this equation, in fact, suggests that


either V1 is null vector or V2 is null vector, but not both