Find the projection of u onto v. $\begin{array} { l }
\mathbf { u } = \langle 3,6 \rangle \
\mathbf { v } = \langle 4,6 \rangle
\end{array}$
A) $13 \langle 72,48 \rangle$
B) $\frac { 1 } { 13 } \langle 3,4 \rangle$
C) $\frac { 13 } { 12 } \langle 48,72 \rangle$
D) $\frac { 1 } { 13 } \langle 48,72 \rangle$
E) $\frac { 12 } { 13 } \langle 48,72 \rangle$

Question

Find the projection of u onto v.​ $\begin{array} { l } 
\mathbf { u } = \langle 3,6 \rangle \
\mathbf { v } = \langle 4,6 \rangle
\end{array}$ ​
A) $13 \langle 72,48 \rangle$
B) $\frac { 1 } { 13 } \langle 3,4 \rangle$
C) $\frac { 13 } { 12 } \langle 48,72 \rangle$
D) $\frac { 1 } { 13 } \langle 48,72 \rangle$
E) $\frac { 12 } { 13 } \langle 48,72 \rangle$

Quizplus · Accepted Answer

The projection of $\mathbf{u}$ onto $\mathbf{v}$ is given by $\text{proj}_{\mathbf{v}}\mathbf{u} = \frac{\mathbf{u} \cdot \mathbf{v}}{\|\mathbf{v}\|^2}\mathbf{v}$. Here, $\mathbf{u} \cdot \mathbf{v} = 3*4 + 6*6 = 12 + 36 = 48$, and $\|\mathbf{v}\|^2 = 4^2 + 6^2 = 16 + 36 = 52$. Thus, $\text{proj}_{\mathbf{v}}\mathbf{u} = \frac{48}{52}\mathbf{v} = \frac{12}{13}\langle 4,6 \rangle$, which simplifies to $\frac{1}{13}\langle 48,72 \rangle$.

Find the Projection of U onto V u=⟨3,6⟩v=⟨4,6⟩\begin{array} { l } \mathbf { u } = \langle 3,6 \rangle \\\mathbf { v } = \langle 4,6 \rangle\end{array}u=⟨3,6⟩v=⟨4,6⟩​

Find the Projection of U onto V $\begin{array} { l } \mathbf { u } = \langle 3,6 \rangle \\\mathbf { v } = \langle 4,6 \rangle\end{array}$