Find two unit vectors that are parallel to the
−plane and are orthogonal to the vector
3 − + 2.
Answers
Answered by
1
Answer:
General solution is
±
(
2
+
c
,
3
c
,
−
3
)
|
(
2
+
c
3
c
−
3
)
|
Particular solutions for + sign, and c =0 and 1, are
1
√
13
(
2
,
0
,
−
3
)
and
1
√
3
(
1
,
1
,
−
1
)
, respectively.
Explanation:
A vector parallel to yz-plane is
p
=
j
+
c
k
=
(
0
,
1
,
c
)
, with c at your
choice..
The other given vector is
q
=
3
i
−
j
+
2
k
=
(
3
,
−
1
,
2
)
Now,
r
=
±
(
p
X
q
)
=
±
(
(
0
,
1
,
c
)
X
(
3
,
−
1
,
2
)
=
±
(
2
+
c
,
3
c
,
−
3
)
is
orthogonal to both
p
and
q
..
Such orthogonal unit vectors, for + sign, and c =0 and 1, are
1
√
13
(
2
,
0
,
−
3
)
and
1
√
3
(
1
,
1
,
−
1
)
, respectively.
The general solution is
±
(
2
+
c
,
3
c
,
−
3
)
|
(
2
+
c
3
c
−
3
)
|
, where c i a parameter
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