Transcribed Image Text: Lets move to three dimensions! Let R(n, 0) be a right-handed rotation by angle 0 about the axis n.3 The rotation matrices

Transcribed Image Text: Lets move to three dimensions! Let R(n, 0) be a right-handed rotation by angle 0 about the axis
n.3 The rotation matrices about the three axes â, ŷ, and ê in three dimensions are
sin 0
cos O
sin 0
Cos O
R(ŷ,0) =
– sin 0
cos 0
R(2,0) =
R(ê, 0) =
sin 0
cos O
Cos O
sin 0
sin 0
cos O
Check that R(î, 7/2), R(ŷ, T /2), and R(ê, T /2) all give the expected result when acting on the
(d)
vector âî.
[Note: First consider a set of coordinate axes: âît to the right of the page, ŷ to the top of the page,
and î coming out of the plane of the page – and determine what a right-handed rotation by 90 degrees
and see if they agree!]
does to the vector âî. Then see what the matrices R do to îî =

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