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, $$	ext{proj}_\mathbf{v}\mathbf{u}=\left(\frac{4(3)+(-5)(-1)}{3^2+(-1)^2}ight)\langle3,-1angle=\left(\frac{17}{10}ight)\langle3,-1angle=\left\langle\frac{51}{10},-\frac{17}{10}ightangle$$

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 $\mathbf { u } = \langle 4 , - 5 \rangle$