  ### Home > PC3 > Chapter Ch8 > Lesson 8.3.5 > Problem8-157

8-157. This problem is a checkpoint for operations with vectors.

Let $\vec { \text{u} } = \langle 1 , - 2 \rangle$, $\vec { \text{v} } = \langle - 5 , - 4 \rangle$, and $\vec { \text{w} } = \langle 4,3 \rangle$. Determine:

1. The direction of $\vec { \text{v} }$.

1. $\left||\vec{\text{w}}|\right|$

Sketch a diagram for each part below and express the resultant vector in component form:

1. $-4\vec{\text{u}}$

1. $3\vec{\text{u}}-\vec{\text{w}}$

1. $\frac { 1 } { 2 } \vec { \text{v} } + 2 \vec { \text{u} }$

Ideally at this point you are comfortable working with these types of problems and can complete them correctly. If you feel that you need more confidence when completing these types of problems, then review the Vector Operations Checkpoint materials available at cpm.org and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.

Answers and extra practice for the Checkpoint problems are located in the Reference Tab of your eBook.