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Kamila [148]
3 years ago
14

Find the scalar and vector projections of b onto a. a=[1,2], b=[-4,1]

Mathematics
1 answer:
VladimirAG [237]3 years ago
6 0

Answer

we have,

a=[1,2],     b=[-4,1]

we need to find projection of b onto a.

scalar projection

     = \dfrac{a.b}{|a|}

     = \dfrac{(1,2).(-4,1)}{\sqrt{1^2+2^2}}

     = \dfrac{1\times (-4)+2\times 1}{\sqrt{1^2+2^2}}

     =\dfrac{-2}{\sqrt{5}}

now, vector projection

     = \dfrac{a.b}{|a|^2}.a

     = \dfrac{(1,2).(-4,1)}{(\sqrt{1^2+2^2})^2}.(1,2)

     = \dfrac{1\times (-4)+2\times 1}{5}.(1,2)

     =\dfrac{-2}{5}.(1,2)

     =(\dfrac{-2}{5},\dfrac{-4}{5})

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Is that correct?

4x = x^2 - 5

x = - 10

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and it does work.  

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