Show that if v 1 , v 2 , and v 3 are mutually orthogonal nonzero vectors in 3-space, and if a vector v in 3-space us expressed as v = c 1 v 1 + c 2 v 2 + c 3 v 3 Then the scalers are given by the formulas c i = v ⋅ v i / v i 2 , i = 1 , 2 , 3
Show that if v 1 , v 2 , and v 3 are mutually orthogonal nonzero vectors in 3-space, and if a vector v in 3-space us expressed as v = c 1 v 1 + c 2 v 2 + c 3 v 3 Then the scalers are given by the formulas c i = v ⋅ v i / v i 2 , i = 1 , 2 , 3
Show that if
v
1
,
v
2
,
and
v
3
are mutually orthogonal nonzero vectors in 3-space, and if a vector v in 3-space us expressed as
v
=
c
1
v
1
+
c
2
v
2
+
c
3
v
3
Then the scalers are given by the formulas
c
i
=
v
⋅
v
i
/
v
i
2
,
i
=
1
,
2
,
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.
University Calculus: Early Transcendentals (4th Edition)
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