Let v 1 = ( − 4 , 0 , 0 , 1 ) , v 2 = ( 1 , 2 , 3 , 4 ) . Determine all vectors in ℝ 4 that are orthogonal to both v 1 and v 2 .Use this to find an orthogonal basis for ℝ 4 that includes the vectors v 1 and v 2 .
Let v 1 = ( − 4 , 0 , 0 , 1 ) , v 2 = ( 1 , 2 , 3 , 4 ) . Determine all vectors in ℝ 4 that are orthogonal to both v 1 and v 2 .Use this to find an orthogonal basis for ℝ 4 that includes the vectors v 1 and v 2 .
Solution Summary: The author explains how to find all vectors in R4 that are orthogonal to both
Let
v
1
=
(
−
4
,
0
,
0
,
1
)
,
v
2
=
(
1
,
2
,
3
,
4
)
. Determine all vectors in
ℝ
4
that are orthogonal to both
v
1
and
v
2
.Use this to find an orthogonal basis for
ℝ
4
that includes the vectors
v
1
and
v
2
.
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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