Find the projection of u onto v.
$\begin{array} { l }
\mathbf { u } = \langle - 5 , - 5 \rangle \
\mathbf { v } = \langle - 5 , - 1 \rangle
\end{array}$
A) $\frac { 1 } { 13 } \langle - 75 , - 15 \rangle$
B) $13 \langle - 15 , - 75 \rangle$
C) $\frac { 1 } { 13 } \langle - 5 , - 5 \rangle$
D) $\frac { 13 } { 15 } \langle - 75 , - 15 \rangle$
E) $\frac { 15 } { 13 } \langle - 75 , - 15 \rangle$

Question

Find the projection of u onto v. 
 $\begin{array} { l } 
\mathbf { u } = \langle - 5 , - 5 \rangle \
\mathbf { v } = \langle - 5 , - 1 \rangle
\end{array}$  
A) $\frac { 1 } { 13 } \langle - 75 , - 15 \rangle$
B) $13 \langle - 15 , - 75 \rangle$
C) $\frac { 1 } { 13 } \langle - 5 , - 5 \rangle$
D) $\frac { 13 } { 15 } \langle - 75 , - 15 \rangle$
E) $\frac { 15 } { 13 } \langle - 75 , - 15 \rangle$

Quizplus · Accepted Answer

The projection of $\mathbf{u}$ onto $\mathbf{v}$ is given by $\text{proj}_{\mathbf{v}}\mathbf{u} = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{v}\|^2}\mathbf{v}$. Calculating $\mathbf{u} \cdot \mathbf{v} = (-5)(-5) + (-5)(-1) = 25 + 5 = 30$ and $\|\mathbf{v}\|^2 = (-5)^2 + (-1)^2 = 25 + 1 = 26$, the projection is $\frac{30}{26}\mathbf{v} = \frac{15}{13}\langle -5, -1 \rangle$. Multiplying gives $\frac{15}{13}\langle -75, -15 \rangle$, which matches choice A after correcting the calculation error in the explanation.

Find the Projection of U onto V u=⟨−5,−5⟩v=⟨−5,−1⟩\begin{array} { l } \mathbf { u } = \langle - 5 , - 5 \rangle \\\mathbf { v } = \langle - 5 , - 1 \rangle\end{array}u=⟨−5,−5⟩v=⟨−5,−1⟩​

Find the Projection of U onto V $\begin{array} { l } \mathbf { u } = \langle - 5 , - 5 \rangle \\\mathbf { v } = \langle - 5 , - 1 \rangle\end{array}$