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}.