Forces as vectors and resolving forcesEdexcel International A Level Maths: Mind map

Exam questions on Forces as vectors and resolving forces

1. A force $\mathbf{F}$ of magnitude 20 N acts in the $x$–$y$ plane at $60^\circ$ above the positive $x$-axis. The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are in the directions of the positive $x$-axis and $y$-axis.
   Write $\mathbf{F}$ in the form $a\mathbf{i}+b\mathbf{j}$, giving $a$ and $b$ exactly.2 marks
2. Two forces act on a particle: $\mathbf{F}_1=(3\mathbf{i}+4\mathbf{j})$ N and $\mathbf{F}_2=(-7\mathbf{i}+2\mathbf{j})$ N.
   Find the angle between the resultant and the vector $\mathbf{j}$, giving your answer to 1 decimal place.2 marks
3. Three forces act on a particle: $\mathbf{F}_1=(2\mathbf{i}-3\mathbf{j})$ N, $\mathbf{F}_2=(p\mathbf{i}+q\mathbf{j})$ N and $\mathbf{F}_3=(-\mathbf{i}+5\mathbf{j})$ N, where $p$ and $q$ are constants. The resultant of the three forces is $(6\mathbf{i}+4\mathbf{j})$ N.
   Find the values of $p$ and $q$.3 marks