If the vertices of a triangle have position vectors a, b, c, what is the condition for the triangle to be right-angled?

If the vertices of a triangle have position vectors a, b, c, what is the condition for the triangle to be right-angled?

• A. (a−b).(b−c) = 0 or (b−c).(c−a) = 0 or (c−a).(a−b) = 0
• B. a.b + b.c + c.a = 0
• C. a × b + b × c + c × a = 0
• D. [a b c] = 0

Answer: A) (a−b).(b−c) = 0 or (b−c).(c−a) = 0 or (c−a).(a−b) = 0

Explanation: The sides of the triangle are represented by vectors (a−b), (b−c), and (c−a). For it to be a right triangle, two sides must be perpendicular, meaning their dot product is zero.