The Projection of "a" along "b" is [tex]\sqrt{20}[/tex] and the Projection of "b" on "a" is [tex]\frac{20}{\sqrt{29} }[/tex]
Given that a = 2i-3j +4k and b = 2i+4k
To find Projection,
Projection of "x" on "Y"=(X vector).(Y unit vecot)
Projection of "a" along "b" = (a vector).(b unit vector)
Projection of "a" along "b" = ( 2i-3j +4k).([tex]\frac{2i+4k}{\sqrt{29} }[/tex])
Projection of "a" along "b" =[tex]\frac{4+16}{\sqrt{20} }[/tex]
Projection of "a" along "b" =[tex]\frac{20}{\sqrt{20} }[/tex]
Projection of "a" along "b" =[tex]\sqrt{20}[/tex]
Projection of "b" along "a" = (b vector).(a unit vector)
Projection of "b" along "a" = ( 2i+4k).([tex]\frac{2i-3j +4k}{\sqrt{29} }[/tex])
Projection of "b" along "a" = [tex]\frac{20}{\sqrt{29} }[/tex]
Therefore,The Projection of "a" along "b" is [tex]\sqrt{20}[/tex] and the Projection of "b" on "a" is [tex]\frac{20}{\sqrt{29} }[/tex]
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