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