Math 54(R) Homework #5 Answer Key
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 =============================  Hill section 3.1  =============================

20.
    (a) R^3
    (b) R^3
    (c) R^3
    (d) The plane x+y-z=0.

22.
    (a) There are tons of correct answers.
        Probably the simplest *geometric* answer is when the origin and the
        tips of the three vectors are coplanar.
    (b) Ditto; these points now have to be coplanar but not collinear.
    (c) Ditto; these points now have to be collinear but not all zero.
    (d) Only when all three vectors are zero.
    (e) No!!

30. ||u||+||v|| = sqrt(14)+sqrt(3) ~= 5.47; ||u+v|| = 5.


 =============================  Hill section 3.2  =============================

20.
     Plus or minus 1/(2sqrt(7)).