using vectors show that the angle in a semicircle is a right angle

Sunanta Achoibam , Meritnation Expert added an answer, on 20/12/10

Hi!

Here is the answer to your question.

Let O (0, 0) be the centre of a semicircle of radius *a*.

The coordinated of any point P on the circle can be written as P (*a* cos * q *, *a* sin * q *) where * q * is the angle formed by OP with positive direction of *x*-axis.

This, means that angle between PA and PB is 90°.

Cheers!

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