COSMOS: Complete Online Solutions Manual Organization System
Chapter 3, Solution 57.
(
M OA = λ OA ⋅ rC/O × P
Have
)
where
From triangle OBC
Since
or
a
2
( OA) x
=
( OA) z
= ( OA ) x tan 30° =
( OA)2
= ( OA ) x + ( OA ) y + ( OAz )
2
a 1
a
=
2 3 2 3
2
2
a
2
a
a = + ( OA) y +
2
2 3
2
∴
Then
rA/O =
and
λ OA =
( OA) y
=
2
2
a2 −
a2 a2
2
−
=a
4
12
3
a
2
a
i +a j+
k
2
3
2 3
2
i+
2
j+
k
3
2 3
P = λ BC P
=
=
( a sin 30°) i − ( a cos30°) k
a
P
i − 3k
2
(
)
rC/O = ai
∴ M OA
1
2
=
1
1
=
=
.
2
1
3 2 3
P
( a )
0
0
2
0 − 3
aP 2
−
(1) − 3
2 3
aP
aP
M OA =
2
2
(
)
( P)
COSMOS Chapter 3 Solution 57
of 1
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