3. Let
0
= (0
,
0
,
0)
,
i
= (1
,
0
,
0)
,
j
= (0
,
1
,
0)
,
k
= (0
,
0
,
1) be vectors in
R
3
. Given a cube with an edge 2 inch
the figure below
O
y
z
x
C
D
B
A
E
F
G
(a) Write down the vectors
--→
OG,
--→
OD,
--→
OE,
--→
OF
as linear combinations of
i
,
j
,
k
.
(b) Let
P, Q, R, S, T, U
be center of the faces
AGFE, GBDF, DCEF, OAEC, OAGB, OBDC
respec-
tively, write the vectors:
--→
OP,
--→
OQ,
--→
OR,
-→
OS,
-→
OT,
--→
OU
as a linear combination of
i
,
j
,
k
.
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