vectors . Vector addition — analytical method . Motion in a plane . Motion in a plane with constant acceleration .
Projectile motion . Uniform circular motion Summary Points to ponder Exercises just as the ordinary numbers * . For example, if the length and breadth of a rectangle are . m and .
m respectively, then its perimeter is the sum of the lengths of the four sides, . m + . m + . m + .
m = . m. The length of each side is a scalar and the perimeter is also a scalar. Take another example: the maximum and minimum temperatures on a particular day are .
°C and . °C respectively. Then, the difference between the two temperatures is . °C.
Similarly, if a uniform solid cube of aluminium of side cm has a mass of . kg, then its volume is – m (a scalar) and its density is . × kg m – (a scalar). A vector quantity is a quantity that has both a magnitude and a direction and obeys the triangle law of addition or equivalently the parallelogram law of addition .
So, a vector is specified by giving its magnitude by a number and its direction. Some physical quantities that are represented by vectors are displacement, velocity, acceleration and force. To represent a vector, we use a bold face type in this book. Thus, a velocity vector can be represented by a symbol v .
Since bold face is difficult to produce, when written by hand, a vector is often represented by an arrow placed over a letter, say r v . Thus, both v and r v represent the velocity vector. The magnitude of a vector is often called its absolute value, indicated by | v | = v . Thus, a vector is represented by a bold face, e.g.
by A, a, p, q, r, ... x, y , with respective magnitudes denoted by light face A, a, p, q, r, ... x, y . .
. Position and Displacement Vectors To describe