Page 79 - Mathematics Class - XII

ACTIVITY 6.2

OBJECTIVE

To verify that angle in a semi-circle is a right angle, using vector method.

MATERIAL REQUIRED
Y Cardboard/drawing board Y Eraser

Y White chart paper Y Wires
Y Adhesive Y Thumb pin
Y Pens Y Paper arrow heads

Y Geometry box

PRE-REQUISITE KNOWLEDGE
1. Knowledge of the concept of dot product of two vectors.
2. Knowledge of the concept of equal vectors.

PROCEDURE
1. Take a cardboard/drawing board of a convenient size and paste a white paper on it.

2. On this paper draw a circle, with centre O and radius = 10 cm.
3. Take any point A on the circumference of the circle as shown in Fig. (a).

4. Take another point Q and fix nails at the points O, A, B, P and Q. Join OP, OA, OB, AP, AQ, BQ, OQ and
BP using wires.
5. Put arrows on OA, OB, OP, AP, BP, OQ, AQ and BQ to show them as vectors, using paper arrow heads,
as shown in the Fig. (b).

Fig. (a) Fig. (b)

DEMONSTRATION

1. Using a protractor, measure the angle between the vectors AP and BP . We see that ∠APB = 90°.

2. Similarly, the angle between the vectors AQ and BQ , i.e., ∠AQB = 90°.
3. Repeat the above process by taking some more points R, S, T, ... on the semi-circles, forming vectors

AR, BR; AS, BS; AT, BT; ..., etc., i.e., angle formed between two vectors in a semi-circle is a right angle.

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