**Unformatted text preview: **= 1, 1, 1, 0. Write
u
v
= w1 + w2
v
where w1 is parallel to and w2 is perpendicular to .
u
u
Answer:
There are several approaches. One is to use vector projection onto to calculate w1 , then
u
subtract to ﬁnd w2 . Another is to use w1 = k , · w2 = 0. Solving the equation above for w2
uu
and using these two equations we have · ( − k . Since only k is unknown in this equation
uv
u
we can solve for k and the rest follows.
Answer: w1 = 1 , 0, 1, 1 and w2 = 1 , 1, 0, − 1
2
2
2
2
5. (20 points) Suppose x(t) = et , y (t) = 2 + sin(2t) and z (t) = 2 + cos(4t). If
w(x, y, z ) =
evaluate xy
+
yz dw
when t = 0.
dt...

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