**|r|**= | (4,5)^{T}| = √(16+25) = 6.40- direction = arc tan{ 5/4 } = 51.34°

Say that you have been given a length and a direction and want to express them as a 2D column vector.

- Draw a sketch.
- Calculate x by projecting the length onto the x-axis

(usually length*cos( θ ) ) - Calculate y by projecting the length onto the y-axis

(usually length*sin( θ ) ) - Check answers against the sketch.

Of course, you can't wait to practice this (it brings back those fond memories of trigonometry.)

A vector has length 4 and orientation 150°. Represent the vector as a column matrix.