4. Exercises

The diagram shows a force and the unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}

Express the force in terms of the unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}

Express each of the forces given below in the form \displaystyle a\mathbf{i}+b\mathbf{j}

a) Find the magnitude of the force 6 \displaystyle \mathbf{i}\displaystyle + 8 \displaystyle \mathbf{j} N, where \displaystyle \mathbf{i} and \displaystyle \mathbf{j} are perpendicular unit vectors.

b) Find the angle, to the nearest degree, between the force and the unit vector \displaystyle \mathbf{i}.

A force is expressed as 9 \displaystyle \mathbf{i}\displaystyle + 10 \displaystyle \mathbf{j} N.

a) Calculate the magnitude of this force.

b) Find the angle between the force and the unit vector \displaystyle \mathbf{i}.

For each force given below find its magnitude and the angle between the force and the unit vector \displaystyle \mathbf{i}.

a) \displaystyle \left( 4\mathbf{i}+3\mathbf{j} \right)\text{ N}

b) \displaystyle \left( 4\mathbf{i}-3\mathbf{j} \right)\text{ N}

c) \displaystyle \left( -2\mathbf{i}+8\mathbf{j} \right)\text{ N}

d) \displaystyle \left( -5\mathbf{i}-7\mathbf{j} \right)\text{ N}

The diagram shows two forces and the unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}.

a) Express each force in the form \displaystyle a\mathbf{i}+b\mathbf{j}.

b) Find the magnitude of the resultant of these two forces.

c) Find the angle between the resultant force and the unit vector \displaystyle \mathbf{i}, and draw a diagram to show the direction of the resultant force.