Problems Let v 1 = ( 1 , 2 , 3 ) , v 2 = ( 1 , 1 , − 1 ) . Determine all nonzero vectors w in ℝ 3 such that { v 1 , v 2 , w } is an orthogonal set. Hence obtain an orthonormal set of vectors in ℝ 3 .
Problems Let v 1 = ( 1 , 2 , 3 ) , v 2 = ( 1 , 1 , − 1 ) . Determine all nonzero vectors w in ℝ 3 such that { v 1 , v 2 , w } is an orthogonal set. Hence obtain an orthonormal set of vectors in ℝ 3 .
Solution Summary: The author explains that an orthogonal set of vectors is called lv_1=(1,2,3)
Let
v
1
=
(
1
,
2
,
3
)
,
v
2
=
(
1
,
1
,
−
1
)
. Determine all nonzero vectors
w
in
ℝ
3
such that
{
v
1
,
v
2
,
w
}
is an orthogonal set. Hence obtain an orthonormal set of vectors in
ℝ
3
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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