Practice Vector Intuition in Math

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

Quick Recap

A mathematical object with both a magnitude (size) and a direction, often drawn as an arrow.

An arrow: how long it is (magnitude) and which way it points (direction).

Example 1

easy
A displacement vector points 3 units east and 4 units north. What is the magnitude of this vector?

Example 2

medium
Vectors \vec{u} = (2, 3) and \vec{v} = (-1, 4). Find \vec{u} + \vec{v} and interpret the result geometrically.

Example 3

easy
What is the difference between a vector and a scalar? Give one example of each.

Example 4

hard
Find the unit vector in the direction of \vec{w} = (3, -4).