Let u 1 = [ 1 1 − 2 ] , u 2 = [ 5 − 1 2 ] , and u 3 = [ 0 0 1 ] .Note that u 1 and u 2 are orthogonal but that u 3 is not orthogonal to u 3 or u 2 . It can be shown that u 3 is not in the subspace W spanned by u 1 and u 2 . Use this fact to construct a nonzero vector v in ℝ 3 that is orthogonal to u 1 and u 2 .
Let u 1 = [ 1 1 − 2 ] , u 2 = [ 5 − 1 2 ] , and u 3 = [ 0 0 1 ] .Note that u 1 and u 2 are orthogonal but that u 3 is not orthogonal to u 3 or u 2 . It can be shown that u 3 is not in the subspace W spanned by u 1 and u 2 . Use this fact to construct a nonzero vector v in ℝ 3 that is orthogonal to u 1 and u 2 .
Solution Summary: The author explains that a nonzero vector v in R3 is orthogonal, but not in the subspace W.
Let u1 =
[
1
1
−
2
]
, u2 =
[
5
−
1
2
]
, and u3 =
[
0
0
1
]
.Note that u1 and u2 are orthogonal but that u3 is not orthogonal to u3 or u2. It can be shown that u3 is not in the subspace W spanned by u1 and u2. Use this fact to construct a nonzero vectorv in ℝ3 that is orthogonal to u1 and u2.
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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