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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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Most popular questions from this chapter

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

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(Hint: Think of the xy-plane as part of 3.)

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(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

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Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is k=1.

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(c) True or False: k=1n1k+1+k=0nk2is equal to k=1nk3+k2+1k+1 .

(d) True or False: k=1n1k+1k=1nk2 is equal to k=1nk2k+1.

(e) True or False: k=0mk+k=mnkis equal tok=0nk.

(f) True or False: k=0nak=a0an+k=1n1ak.

(g) True or False: k=110ak2=k=110ak2.

(h) True or False: k=1nex2=exex+12ex+16.

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