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Consider the position vector i=1,0in 2. Describe the set of position vectors vin 2with the property thatprojiv=i.

Short Answer

Expert verified

Any position vector of the typev=1,bsatisfies the conditionprojiv=i.

Step by step solution

01

Step 1:Given information

the position vector i=1,0in2

02

Step 2:Simplification

Consider the position vectori=1,0in2.

The vector projection ofvonto u is given by:

projuv=u·vu2u

Assume the position vectors ofv=a,bandprojiv=i.

Therefore

projiv=i(Given condition)

1·vi2i=i(Substitution)

1,0·a,b12+02i=i(Simplify)

1a=1

The equation (1) is satisfied fora=1.

The vectorvin3has the position vectorv=1,bso that projiv=iholds.

Thus, any position vector of the typev=1,bsatisfies the conditionprojiv=i.

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