Practice Direction in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The orientation of movement or facing in space, independent of speed or distance—where something points.

North, south, east, west—or the way an arrow points, regardless of how long the arrow is.

Example 1

easy
A vector points from the origin to the point (1, 1). What angle does it make with the positive x-axis?

Example 2

medium
Two vectors: \vec{a} = (1, 0) (east) and \vec{b} = (0, -1) (south). What is the angle between them?

Example 3

easy
Do the vectors (2, 4) and (1, 2) point in the same direction? Explain.

Example 4

hard
A ship sails N30°E (30° east of north). Express this direction as a unit vector in the standard (x, y) coordinate system where x is east and y is north.
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