SCALARS AND VECTORS

SCALARS AND VECTORS

• Vectors are quantities which have magnitude and direction.
•  Example: velocity, displacement, acceleration, force, electric field strength and momentum.
•  Scalar are quantities that have magnitude only.
•  Example: mass, temperature and density.

Addition and subtraction of vectors

•  A vector may be represented by an arrow.
•  The addition of two vectors P and Q is a new vector, that is resultant vector.
•  The resultant vector can be determined using :

             i. method of parallelogram of vectors.
            ii. Method of triangle vectors.

•   Subtraction of vectors is done by using the process of addition.

Triangle of vectors
1. Use a possible scale to draw vector P.
2. From the head of vector P draw a line to represent the vector Q.
3. Complete the triangle. The line from the tail of vector P
    to the head of vector Q represents the sum (P + Q) in magnitude and
    direction.

Relative velocity

•   Subtraction of vectors is used to find the relative velocity between two objects.
•  with velocities v_A = 5 m s^-1  and v_B = 3 m s^-1 respectively.
•   A passenger in car B sees car A in front of it moving away at a speed 2 m s^-1.
• Velocity A relative to B = V_A- V_B 
• A passenger in car A sees car B moving backwards at a speed of 2 m s^-1.   
• Velocity B relative to A  = V_B- V_A 

Resolving a vector

• The two mutually perpendicular components of a vector R are of magnitude;

                               R_x = R cos θ

                              R_y = R sin θ