Question

Prove that vectors a=2i-j+k,b=i-3j-5k and c=3i-4j-4k​

Answer 1

Answer:

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.Read more on Sarthaks.com - https://www.sarthaks.com/498144/show-that-the-points-are-a-2i-j-k-b-i-3j-5k-c-3i-4j-4k-the-vertices-of-a-right-angled-triangle