Question 733666: 1)u×u>=0 and u×u=0 if and only if u=0 prove theorem?
2)Show that there are no vectors u and v such that ||u||=1 ||v||=2 and u×v=3?
3)prove that u is orthogonal to v-PROJu(v) for all vectors u and v in Rn,where u(no=)0 ?
4)find the point R on L that is closest to Q in exercises 27.
(27) Q=(2,2),L with equation [X y]=[-1 2]+t[1 -1] ?
5)prove the Following properties of the cross product
a)u×(v×w)=(U×V)×w
B) U×(v×w)=(u×w)v-(u×v)w
C)||U×V||2=||U||2||V||2-(U×V)2
6)Let u and v be vectors in R3 and let @ be the angle between u and v.
A) prove that ||U×V||=||u|| ||v||sin@
B)prove that the area A of the triangle determined by u and v is givien by A=1/2||u×v||
C)use the result in parr (b) to compute the area of the traingle With vertices A=(1,2,1),B=(2,1,0) and C=(5,-1,3) ?
7)find the check digit d in the given International standard book number(isbn-10)
(0,3,8,7,9,7,9,9,3,d)
8)a) prove that if a transposition error is made in the fourth and fifth entries of the ISBN-10(0,6,7,9,7,6,2,9,0,6) the error will be detected.
B) prove that if a transposition error is made in any two adjacent entries of the ISBN-10in part(a) the error will be detected
C) prove, in general, that the ISBN-10 code will Always detect a transposition erroe involving two adjacent entries. ??
Please help me
Answer by lynnlo(4176)   (Show Source):
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