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).
Showing a random 20 of 50 problems.
Example 1
easyWhich is a vector: '5 km' or '5 km north'?
Example 2
easyWhat is the difference between a vector and a scalar? Give one example of each.
Example 3
easyScale the vector by the scalar .
Example 4
mediumFind the magnitude of .
Example 5
easyFind the magnitude of .
Example 6
easyA displacement vector points 3 units east and 4 units north. What is the magnitude of this vector?
Example 7
hardFind the unit vector in the direction of .
Example 8
challengeA person walks then . Compare the total distance walked with the magnitude of total displacement, and explain the difference.
Example 9
easyClassify as vector or scalar: ' mph east'.
Example 10
mediumTwo vectors have the same direction but different magnitudes. Are they equal?
Example 11
mediumA car drives km. What is the straight-line distance traveled?
Example 12
easyWhat is the magnitude of the zero vector ?
Example 13
mediumA vector goes from point to point . Write it in component form.
Example 14
mediumFind the magnitude of the 3D vector .
Example 15
hardIf , , and , what is the angle between and ?
Example 16
hardFind a unit vector perpendicular to in the plane.
Example 17
mediumSubtract: .
Example 18
easyA vector has two key properties. Name them.
Example 19
mediumWhy must displacement be a vector but distance only a scalar?
Example 20
hardTwo vectors of magnitude each make a angle. Find the magnitude of their sum using the law of cosines.