Let t be a fixed real number and let c = cos t , s = sin t , x = ( c , c s , c s 2 , ... , c s n − 1 , s n ) T Show that x is a unit vector in ℝ n + 1 . Hint : 1 + s 2 + s 4 + ⋅ ⋅ ⋅ + s 2 n − 2 = 1 − s 2 n 1 − s 2
Let t be a fixed real number and let c = cos t , s = sin t , x = ( c , c s , c s 2 , ... , c s n − 1 , s n ) T Show that x is a unit vector in ℝ n + 1 . Hint : 1 + s 2 + s 4 + ⋅ ⋅ ⋅ + s 2 n − 2 = 1 − s 2 n 1 − s 2
Solution Summary: The author explains that x is a unit vector in space Rn+1.
Let t be a fixed real number and let
c
=
cos
t
,
s
=
sin
t
,
x
=
(
c
,
c
s
,
c
s
2
,
...
,
c
s
n
−
1
,
s
n
)
T
Show that x is a unit vector in
ℝ
n
+
1
.
Hint:
1
+
s
2
+
s
4
+
⋅
⋅
⋅
+
s
2
n
−
2
=
1
−
s
2
n
1
−
s
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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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY