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What geometric relationship must two vectors have in order foru+v=u+v ?

Short Answer

Expert verified

The geometric relationship between the vectors is that they are parallel to each other and are in same direction.

Step by step solution

01

Step 1:Given information

The given expression isu+v=u+v

02

Step 2:Simplification

Consider the non-zero vectorsuandv.

The objective is to find the geometric relationship between two vectors ifu+v=u+v.

To find the relationship, consider the valueu+v.

The expressionu+vgives:

u+v2=(u+v)·(u+v)

u+v2=u2+v2+2uvcosθ

Forθ=0°, the equation (1) reduces to:

u+v2=u2+v2+2uv

u+v2=(u+v)2

u+v=u+v

The resultu+v=u+vholds whenθ=0°.

Therefore, the geometric relationship between the vectors is that they are parallel to each other and are in same direction.

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