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Inner Product Spaces and Orthogonality
Inner Product Spaces and Orthogonality
6 questions
Difficulty 2-5
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Foundation
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3 foundation
3 intermediate
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foundation (2/10)
conceptual
The dot product of two vectors
u
,
v
∈
R
n
computes what geometric quantity?
Hide and think first
A.
The total length traced by
u
when slid along
v
, measured as a scalar
B.
The volume of the parallelogram spanned by
u
and
v
in 2D space
C.
The product of their magnitudes times the cosine of the angle between them:
u
⋅
v
=
∥
u
∥∥
v
∥
cos
θ
D.
The minimum distance from the origin to the line connecting
u
and
v
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