Find the projection of u onto v. $\begin{array} { l }
\mathbf { u } = \langle 0,4 \rangle \
\mathbf { v } = \langle 3,20 \rangle
\end{array}$
A) $\frac { 1 } { 409 } \langle 0,3 \rangle$
B) $409 \langle 1600,240 \rangle$
C) $\frac { 80 } { 409 } \langle 240,1600 \rangle$
D) $\frac { 409 } { 80 } \langle 240,1600 \rangle$
E) $\frac { 1 } { 409 } \langle 240,1600 \rangle$

Question

Find the projection of u onto v.​ $\begin{array} { l } 
\mathbf { u } = \langle 0,4 \rangle \
\mathbf { v } = \langle 3,20 \rangle
\end{array}$ ​
A) $\frac { 1 } { 409 } \langle 0,3 \rangle$
B) $409 \langle 1600,240 \rangle$
C) $\frac { 80 } { 409 } \langle 240,1600 \rangle$
D) $\frac { 409 } { 80 } \langle 240,1600 \rangle$
E) $\frac { 1 } { 409 } \langle 240,1600 \rangle$

Quizplus · Accepted Answer

The projection of u onto v is given by $\text{proj}_v \mathbf{u} = \frac{\mathbf{u} \cdot \mathbf{v}}{\mathbf{v} \cdot \mathbf{v}} \mathbf{v}$. Calculating, $\mathbf{u} \cdot \mathbf{v} = 0 \cdot 3 + 4 \cdot 20 = 80$ and $\mathbf{v} \cdot \mathbf{v} = 3^2 + 20^2 = 409$. Thus, $\text{proj}_v \mathbf{u} = \frac{80}{409} \langle 3, 20 \rangle = \frac{1}{409} \langle 240, 1600 \rangle$.

Find the Projection of U onto V u=⟨0,4⟩v=⟨3,20⟩\begin{array} { l } \mathbf { u } = \langle 0,4 \rangle \\\mathbf { v } = \langle 3,20 \rangle\end{array}u=⟨0,4⟩v=⟨3,20⟩​

Find the Projection of U onto V $\begin{array} { l } \mathbf { u } = \langle 0,4 \rangle \\\mathbf { v } = \langle 3,20 \rangle\end{array}$