Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, $ \operatorname{proj}_{\mathbf{v}} \mathbf{u} $.
-$\mathbf { u } = \langle 5 , - 5 \rangle , \mathbf { v } = \langle 6,8 \rangle$
A) $\langle 6,8 \rangle + \langle - 1 , - 13 \rangle$
B) $\langle 1.5,2 \rangle + \langle 3.5 , - 7 \rangle$
C) $\langle - 0.6 , - 0.8 \rangle + \langle 5.6 , - 4.2 \rangle$
D) $\langle 3,4 \rangle + \langle - 8,6 \rangle$

Question

Quizplus · Accepted Answer

The vector projection of $\mathbf{u}$ onto $\mathbf{v}$ is given by $\operatorname{proj}_{\mathbf{v}} \mathbf{u} = \frac{\mathbf{u} \cdot \mathbf{v}}{\mathbf{v} \cdot \mathbf{v}} \mathbf{v}$. Calculating this gives $\langle -0.6, -0.8 \rangle$. The orthogonal vector is found by subtracting this projection from $\mathbf{u}$, resulting in $\langle 5.6, -4.2 \rangle$.

Write the Vector U as a Sum of Two Orthogonal proj⁡vu \operatorname{proj}_{\mathbf{v}} \mathbf{u} projv​u

Write the Vector U as a Sum of Two Orthogonal $\operatorname{proj}_{\mathbf{v}} \mathbf{u}$