Question

12. Show that the points A(2î – ĵ + k^), B(î – 3ị – 5k^), and C(3î – 4j^– 4k^) are the vertices of right angled
triangle.​

Answer 1

Step-by-step explanation:

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.