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Home | 18.013A | Chapter 3 | Section 3.3 |
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Express the component of perpendicular to in terms of dot products.
Solution:
The component of
perpendicular to
is the magnitude of the projection of
perpendicular to
. By
definition
this projection is
minus the projection of
in the direction of
.
But the projection of
in the direction of
is
.
The projection of
normal to
is then
, the component of
normal to
is then the square root of the dot product of this projection with itself, or
.
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