TOPIC 6: VECTORS ~ MATHEMATICS FORM 4
Displacement and Positions of Vectors
are many Vector quantities, some of which are: displacement, velocity,
acceleration, force, momentum, electric field and magnetic field.
the x —plane all vectors with initial points at the origin and their
end points elsewhere are called position vectors. Position vectors are
named by the coordinates of their end points.
The magnitude / modules of a vector is the size of a vector, it is a
scalar quantity that expresses the size of a vector regardless of its
are two method used to read bearings, in the first method all angles
are measured with reference from the North direction only where by the
North is taken as 000, the east 090, the South is 180 and West 270
the bearing of point B from point A is measured from the north
direction at point A to the line joining AB and that of A from B is
measured from the North direction at point B to the line joining BA.
this method the location of places is found by reading an acute angle
from the north eastwards or westwards and from the south eastwards or
from Iringa. Sketch the position of these towns relative to each other,
hence calculate the magnitude and direction of the displacement from
Makambako to Mikumi.
by using the scale AB is approximately14.3 cm Therefore AB = 14.3x 20
km = 286km and the bearing is obtained a protractor which is about N51E
two vectors involves joining two vectors such that the initial point of
the second vector is the end point of first vector and the resultant is
obtained by completing the triangle with the vector whose initial point
is the initial point of the first vector and whose end points the end
point of the second vector.
two vectors have a common initial point say P, then their resultant is
obtained by completing a parallelogram, where the two vectors are the
sides of the diagonal through P and with initial point at P
you want to add more than two vectors, you join the end point to the
initial point of the vectors one after another and the resultant is the
vector joining the initial point of the first vector to the end point of
the last vector
when subtracting one vector from another the result obtained is the
same as that of addition but to the opposite of the other vector.
a vector U has a magnitude m units and makes an angleθwith a positive x
axis, then doubling the magnitude of U gives a vector with magnitude
from the dormitory to the parade ground and then he walks 100m due east
to his classroom. Find his displacement from dormitory to the
- Determine the magnitude and direction of their resultant.
- Calculate the magnitude and direction of the opposite of the resultant force.
- The resultant of U + V + W
- The magnitude and direction of the resultant calculated in part (a) above.
A boat moves with a velocity of 10km/h upstream against a downstream
current of 10km/h. Calculate the velocity of the boat when moving down
[if !supportLists]–>4. <!–[endif]–>Calculate the magnitude
and direction of the resultant of the velocities V1=5i + 9j,V2 = 4i + 6j and V3 = 4i – 3j where i and j are unit vectors of magnitude 1m/s in the positive directions of the x and y axis respectively.