Graph a resultant vector using the triangle method (Tutorial Only)

Learning Objectives Define a vector and identify its magnitude and direction. Accurately identify the 'head' and 'tail' of a vector arrow. State and apply the 'head-to-tail' rule for graphical vector addition. Construct a resultant vector for two given vectors using a ruler and protractor. Draw the resultant vector from the tail of the first vector to the head of the second vector. Determine the magnitude and direction of a resultant vector from a scale drawing. Interpret the meaning of a resultant vector in a simple context, such as displacement or force. Imagine you walk 5 blocks east, then 4 blocks north. How would you describe your final position relative to where you started? 🗺️ Vectors give us the tools to answer this precisely! This tu...

TermDefinitionExample VectorA quantity that has both magnitude (size) and direction. It is represented graphically by an arrow.A displacement of 10 km North. The magnitude is 10 km, and the direction is North. ScalarA quantity that has only magnitude, but no direction.A distance of 10 km. We know how far, but not in which direction. MagnitudeThe length or size of a vector. It is always a positive scalar value.For a velocity vector of 60 km/h East, the magnitude is 60 km/h. DirectionThe orientation of a vector in space, often expressed as an angle from a reference line or a compass bearing.For a force vector of 25 N at 30° above the horizontal, the direction is 30° above the horizontal. Resultant VectorThe vector sum of two or more vectors. It represents the single vector that would have t...

Vector Addition Notation \vec{R} = \vec{A} + \vec{B} This is the mathematical expression for adding vector A and vector B to get a resultant vector R. The arrow above each letter signifies that it is a vector quantity. Triangle Method (Head-to-Tail Rule) To add \vec{A} and \vec{B}, place the tail of \vec{B} on the head of \vec{A}. This is the fundamental rule for graphical vector addition. You draw the first vector, and then start drawing the second vector where the first one ended. The vectors are drawn one after another in a chain. Drawing the Resultant The resultant \vec{R} is drawn from the tail of the first vector (\vec{A}) to the head of the last vector (\vec{B}). After arranging the vectors head-to-tail, the resultant 'closes the triangle'. It repres...