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6.3.3 Application of dot and cross products in Geometry

Chapter 6: Chapter 6 · MATHEMATICS-VOLUME 1 · EN medium

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Example . (Apollonius's theorem) If D is the midpoint of the side BC of a triangle ABC , show by vector method that (| | ) AB AC AD BD Let A be the origin, b be the position vector of B and c  be the position vector of C . Now D is the midpoint of BC , and so the, position vector of D is . Therefore, we have Fig. . Fig. .

📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 235

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Example . (Apollonius's theorem) If D is the midpoint of the side BC of a triangle ABC , show by vector method that (| | ) AB AC AD BD Let A be the origin, b be the position vector of B and c  be the position vector of C . Now D is the midpoint of BC , and so the, position vector of D is . Therefore, we have Fig. . Fig. .

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