Question

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of PQ

Answer 1

Note that a vector \(V\) from point \(P\) to \(Q\) is:
\[
Q-P=V
\]So, we have that:
\[
V=Q-P=<6,9>-<5, 8>=<1,1>
\]So:
\[
V=<1,1>=1{\bf{i}}+1\bf{j}
\]The magnitude is given by:
\[
|V|=\sqrt{x^2+y^2}=\sqrt{1+1}=\sqrt{2}
\]