Find vector with same direction but different length
Answers
Answered by
0
Answer:
(
−
24
√
177
,
21
√
177
,
24
√
177
)
Explanation:
The idea is based on a concept of scaling and similarity.
Any vector that "has the same direction" as
(
−
8
,
7
,
8
)
has all the coordinates proportional to this given vector and, therefore, can be described by coordinates
(
−
8
f
,
7
f
,
8
f
)
where
f
is a scaling factor.
All we need now is to find a scaling factor that leads to a vector with the length
3
.
The length of a vector with coordinates
(
−
8
f
,
7
f
,
8
f
)
equals to
√
64
f
2
+
49
f
2
+
64
f
2
=
f
⋅
√
177
So, if we want the length to be equal to
3
, we should choose
f
=
3
√
177
The coordinates of a vector with the same direction as
(
−
8
,
7
,
8
)
but with the length
3
will be
(
−
24
√
177
,
21
√
177
,
24
√
177
)
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