MATH 200 ASSIGNMENT 1
1. Show that the vector orth~a~b := ~b−proj~a~b is orthogonal to ~a, where proj~a~b
is the projection of ~b on ~a . (orth~a~b is called the projection of ~b orthogonal
to ~a.)
2. Find the angle between a diagonal of a cube and one of its edges.
3. If ~c = |~a|~b + |~b|~a, where ~a, ~b and ~c are all nonzero vectors, show that ~c
bisects the angle between ~a and ~b.
4. Prove the Parallelogram Law:
|~a + ~b|2 + |~a − ~b|2 = 2|~a|2 + 2|~b|2 .
5. Show that if ~u + ~v and ~u − ~v are orthogonal, then the vectors ~u and ~v
have the same length.
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