In Exercises 9 − 12 , express the given vector v in terms of the orthogonal basis B = { u 1 , u 2 , u 3 } , where u 1 , u 2 , and u 3 are as in Exercise 1 . v = [ 3 3 3 ] . u 1 = [ 1 1 1 ] , u 2 = [ − 1 0 1 ] , u 3 = [ − 1 2 − 1 ] .
In Exercises 9 − 12 , express the given vector v in terms of the orthogonal basis B = { u 1 , u 2 , u 3 } , where u 1 , u 2 , and u 3 are as in Exercise 1 . v = [ 3 3 3 ] . u 1 = [ 1 1 1 ] , u 2 = [ − 1 0 1 ] , u 3 = [ − 1 2 − 1 ] .
Solution Summary: The author explains how the vector v is expressed in terms of the orthogonal basis B=u_1.
In Exercises
9
−
12
, express the given vector
v
in terms of the orthogonal basis
B
=
{
u
1
,
u
2
,
u
3
}
, where
u
1
,
u
2
, and
u
3
are as in Exercise
1
.
v
=
[
3
3
3
]
.
u
1
=
[
1
1
1
]
,
u
2
=
[
−
1
0
1
]
,
u
3
=
[
−
1
2
−
1
]
.
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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