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} $.
-$$\mathbf { u } = \langle 6 , - 9 \rangle , \mathbf { v } = \langle - 9 , - 3 \rangle$$
A) $\langle - 9 , - 3 \rangle + \langle 15 , - 6 \rangle$
B) $\langle 3,1 \rangle + \langle 3 , - 10 \rangle$
C) $\langle 2.7,0.9 \rangle + \langle 3.3 , - 9.9 \rangle$
D) $\langle - 6 , - 2 \rangle + \langle 12 , - 36 \rangle$

Question

Quizplus · Accepted Answer

The vector projection of $\mathbf{u}$ onto $\mathbf{v}$ is given by $\operatorname{proj}_{\mathbf{v}} \mathbf{u} = \left( \frac{\mathbf{u} \cdot \mathbf{v}}{\mathbf{v} \cdot \mathbf{v}} \right) \mathbf{v}$. Calculating this gives $\langle 2.7,0.9 \rangle$. The orthogonal vector to this projection that, when added to it, gives $\mathbf{u}$ is $\langle 3.3 , - 9.9 \rangle$.

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 $\operatorname{proj}_{\mathbf{v}} \mathbf{u}$