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

Question

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

Answer 1

If A, B and C are the vertices of the right angle triangle

So,

In a right angle triangle

Where AB is the hypotenuse

BC is the perpendicular and CA is the base

Vertices of the triangle are given bellow

41 = 35 + 6

41 = 41

LHS = RHS