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experimentX
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experimentX
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experimentX
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\[ \cos \theta = \frac{<u, v>}{||u||\; ||v||}\]
experimentX
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so you have the component of u along v is
\[ \large \frac{||u||\;v}{||v||} \times \frac{<u, v>}{||u||\; ||v||}= \frac{v <u,v>}{||v||^2} = \frac{v <u,v>}{<v,v>}\]
experimentX
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using vector law of addition we get .. the component perpendicular to V is
\[V - \frac{V <U,V>}{<V,V>} \]
experimentX
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experimentX
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experimentX
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you can check for dot product ... and show be able to verify which should be perpendicular to which and ...same goes for parallel.
Callisto
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experimentX
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Callisto
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Once we find u along v, we can express u as a linear combination of v and v⊥?!
experimentX
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yes .. .lol, that will be equal to u
experimentX
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use brackets to separate it ... and don't do arithmetic.