Show that the points A, B and C with position vectors, respectively form the vertices of a right angled triangle.


O be the origin,
Let



And



Now we find the vectors




……….(1)




………….(2)




……….(3)


Adding equations (1), (2) and (3)




Therefore, ABC form a triangle.


Now, we want to prove that it is a right angled triangle.







Therefore, the triangle satisfies the Pythagoras theorem. Hence, proved the given vectors form a right angled triangle.


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