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1, Let a = 2i-3j +4k and b = 2i+4k
a) Find the Projection of a "a" long "b"
b) Find the Projection of "b" along "a"​

Sagot :

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]

Learn more about Projection here:

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