In C [ 0 , 1 ] , with inner product defined by (3), consider the vectors 1 and x . Find the angle θ between 1 and x . Determine the vector projection p of 1 onto x and verify that 1 − p is orthogonal to p . Pythagorean law holds. Compute ‖ 1 − p ‖ , ‖ 1 ‖ and verify that the Pythagorean law holds.
In C [ 0 , 1 ] , with inner product defined by (3), consider the vectors 1 and x . Find the angle θ between 1 and x . Determine the vector projection p of 1 onto x and verify that 1 − p is orthogonal to p . Pythagorean law holds. Compute ‖ 1 − p ‖ , ‖ 1 ‖ and verify that the Pythagorean law holds.
Solution Summary: The author calculates the angle theta between the vectors 1andx.
In
C
[
0
,
1
]
,
with inner product defined by (3), consider the vectors 1 and x.
Find the angle
θ
between 1 and x.
Determine the vector projection p of 1 onto x and verify that
1
−
p
is orthogonal to p. Pythagorean law holds. Compute
‖
1
−
p
‖
,
‖
1
‖
and verify that the Pythagorean law holds.
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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