Let w denote the projection from part (a). Suppose you have a calculator that ca

Question

Let w denote the projection from part (a). Suppose you have a calculator that calculates decimal expansions of numbers completely correctly up to 127 digits. Will this calculator allow you to tell the difference between v and w? Explain your answer clearly and carefully or feel the grader’s wrath. (Note: you should be able to answer this even if you made silly – non-conceptual – mistakes on part (a).)

Explanation / Answer

normal of the plane x- 9 y +10200 z=0 is n=<1,-9 ,10200 >

v=<0,0,1>

projection of v on to n

=(v.n)n/|n|2

=(<0,0,1>.<1,-9 ,10200 >)<1,-9 ,10200 >/(12+(-9)2 +(10200)2)

=(0+0+10200)<1,-9 ,10200 >/(10400) (since 10200>>>>>>12+(-9)2)

=(10200)<1,-9 ,10200 >/(10400)

=<1,-9 ,10200 >/(10200)

=<10-200,-9*10-200 ,1 >

calculator wont tell the difference between v,w. because here we get 200 decimal places

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