Find the projection of u onto v if $\mathbf { u } = \langle 4 , - 5 \rangle$ , $\mathbf { v } = \langle 3 , - 1 \rangle$
A) $\left\langle \frac { 51 } { \sqrt { 10 } } , \frac { - 17 } { \sqrt { 10 } } \right\rangle$
B) $\left\langle \frac { - 51 } { \sqrt { 10 } } , \frac { - 17 } { \sqrt { 10 } } \right\rangle$
C) $\left\langle \frac { 51 } { \sqrt { 10 } } , \frac { - 51 } { \sqrt { 10 } } \right\rangle$
D) $\left\langle \frac { 17 } { \sqrt { 10 } } , \frac { - 17 } { \sqrt { 10 } } \right\rangle$
E) $\left\langle \frac { 17 } { \sqrt { 10 } } , \frac { 17 } { \sqrt { 10 } } \right\rangle$

Question

Find the projection of u onto v if $\mathbf { u } = \langle 4 , - 5 \rangle$ , $\mathbf { v } = \langle 3 , - 1 \rangle$
A)  $\left\langle \frac { 51 } { \sqrt { 10 } } , \frac { - 17 } { \sqrt { 10 } } \right\rangle$
B) $\left\langle \frac { - 51 } { \sqrt { 10 } } , \frac { - 17 } { \sqrt { 10 } } \right\rangle$
C)  $\left\langle \frac { 51 } { \sqrt { 10 } } , \frac { - 51 } { \sqrt { 10 } } \right\rangle$
D)  $\left\langle \frac { 17 } { \sqrt { 10 } } , \frac { - 17 } { \sqrt { 10 } } \right\rangle$
E)  $\left\langle \frac { 17 } { \sqrt { 10 } } , \frac { 17 } { \sqrt { 10 } } \right\rangle$

Quizplus · Accepted Answer

The projection of u onto v is given by $$	ext{proj}_\mathbf{v}\mathbf{u}=\left(\frac{\mathbf{u}\cdot\mathbf{v}}{\Vert\mathbf{v}\Vert^2}ight)\mathbf{v}$$So, $$	ext{proj}_\mathbf{v}\mathbf{u}=\left(\frac{4(3)+(-5)(-1)}{3^2+(-1)^2}ight)\langle 3,-1angle$$$$=\left(\frac{12+5}{9+1}ight)\langle 3,-1angle$$$$=\left(\frac{17}{10}ight)\langle 3,-1angle$$$$=\left\langle \frac{51}{10},-\frac{17}{10}ightangle$$

Find the Projection of U onto V If u=⟨4,−5⟩\mathbf { u } = \langle 4 , - 5 \rangleu=⟨4,−5⟩

Find the Projection of U onto V If $\mathbf { u } = \langle 4 , - 5 \rangle$