Find the scalar and vector projections of b onto a. a = 4, 7, −4 b = 3, −1, 1 scalar projection of b onto a vector projection of b onto a

Answer:[tex]comp_{\vec{a}}\vec{b}=0.11 [/tex][tex]proj_{\vec{a}}\vec{b}=\left ( \frac{4}{81},\frac{7}{81},\frac{-4}{81} \right )[/tex]  Step-by-step explanation:a=(4,7,-4) b=(3,-1,1)Scalar projection of b onto a[tex]comp_{\vec{a}}\vec{b}=\frac{a\cdot b}{|a|}[/tex][tex]a\cdot b=\left ( 4\times 3 \right )+\left ( 7\times -1 \right )+\left ( -4\times 1 \right )=1[/tex][tex]|a|=\sqrt{4^2+7^2+4^2}=9[/tex][tex]comp_{\vec{a}}\vec{b}=\frac{a\cdot b}{|a|}=\frac{1}{9}\\\Rightarrow comp_{\vec{a}}\vec{b}=0.11 [/tex] Vector projection of b onto a[tex]proj_{\vec{a}}\vec{b}=\frac{a\cdot b}{|a|^2}\cdot a[/tex][tex]\frac{a\cdot b}{|a|}=\frac{1}{9}[/tex][tex]\frac{a\cdot b}{|a|^2}\cdot a=\frac{1}{81}\left ( {4},{7},{-4} \right )[/tex][tex]proj_{\vec{a}}\vec{b}=\left ( \frac{4}{81},\frac{7}{81},\frac{-4}{81} \right )[/tex]