The points AAA, B B\,B and C C\,C have position vectors a=−i+4j\mathbf{a} = -\mathbf{i} + 4\mathbf{j}a=−i+4j, b=5i+2j\mathbf{b} = 5\mathbf{i} + 2\mathbf{j}b=5i+2j and c=3i−4j\mathbf{c} = 3\mathbf{i} - 4\mathbf{j}c=3i−4j
Show that triangle ABC ABC\,ABC is right-angled, stating at which vertex the right angle lies.
Find the area of triangle ABCABCABC.