Question

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

Answer 1

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

     = $\dfrac{a.b}{|a|^2}.a$

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

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

     =$\dfrac{-2}{5}.(1,2)$

     =$(\dfrac{-2}{5},\dfrac{-4}{5})$