Question

Show that the points are A(2i - j + k), B(i - 3j - 5k), C(3i - 4j - 4k) the vertices of a right angled triangle.

Answer 1

We have vector(AB) =(1 - 2)i + (-3 + 1)j + (-5 - 1)k = - i - 2j - 6k

vector (BC) = (3 - 1)i + (-4 + 3)j + (-4 + 5)k = 2i - j + k

and vector(CA) = (2 - 3)i + (-1 + 4)j + (1 + 4)k = - i + 3j + 5k

Then |vector AB|2 = 41, |vector BC|2 = 6, |vector CA|2 = 35

⇒ |vector AB|2 = |vectorBC|2 + |vector CA|2

Hence, the triangle is a right angled triangle.