Question

Find the component form and magnitude of vector RS.
R=(8,-8) S=(4,7)
Thank you!

Answer 1

`\stackrel{R}{(\stackrel{x_1}{8}~,~\stackrel{y_1}{-8})}\qquad \stackrel{S}{(\stackrel{x_2}{4}~,~\stackrel{y_2}{7})}~\hfill \stackrel{\textit{component form}}{(x_2-x_1~~,~~y_2-y_1)} \\\\[-0.35em] ~\dotfill\\\\ (4-8~~,~~7-(-8))\implies (-4~~,~~7+8)\implies \stackrel{\textit{component form}}{(\underset{a}{-4}~~,~~\underset{b}{15})} \\\\\\ ||RS||=√(a^2+b^2)\implies ||RS||=√((-4)^2+15^2)\implies ||RS||=√(241)`