Vector Addition Notes

► A scalar quantity is a number or measurement which has only a magnitude (size)—examples: Time, mass, volume ► A vector quantity is a number or measurement which has both a magnitude (size) and a direction—examples: velocity, force, accel.

Vectors ► A vector is represented by an arrow pointing in the direction of the measurement with a length which corresponds to the magnitude of the measurement

Scalars vs. Vectors ► Scalars are added using arithmetic addition. Vectors are added using trigonometric (vector) addition.

Vector Addition ► In Vector Addition, vectors should be drawn “tip to tail”. The tail end of a vector is drawn on the arrow end of the previous vector. ► Only two vectors can be added at a time this way.

Vector Addition ► The resultant (the answer you get from adding the two vectors together) is the vector which goes from the first tail to the last tip. ► You can then use trigonometric laws and definitions to find the magnitude and direction of the resultant.

Vector Addition ► The two vectors which are added together are called the component vectors and the answer is the resultant vector.

Vector Addition ► The reverse process (taking one vector and breaking it apart into two vectors which would add together to give the first) is called vector resolution ► To do this make a right triangle with the initial vector as the hypotenuse.

Vector Subtraction ► Vector Subtraction is identical to vector addition, except that you add the negative vector (which is the same magnitude, but opposite direction)

Equilibrium ► Equilibrium is a situation in which opposite Force vectors cancel one another out and there is no net force or acceleration ► An “equilibrant” is a vector which causes equilibrium, and is always equal and opposite to the resultant vector

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