If a, b, c are unit vectors such that a + b + c = 0, find the value of a.b + b.c + c.a. A. 3/2 B. −3/2 C. 0 D. 3 Answer: B) −3/2 Explanation: |a + b + c|² = 0. Expanding: |a|² + |b|² + |c|² + 2(a.b + b.c + c.a) = 0. Since they are unit vectors, 1 + 1 + 1 + 2(a.b + b.c + c.a) = 0, leading to a.b + b.c + c.a = −3/2.

imo class 12 vector algebra

If a, b, c are unit vectors such that a + b + c = 0, find the value of a.b + b.c + c.a.

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If a, b, c are unit vectors such that a + b + c = 0, find the value of a.b + b.c + c.a.

A. 3/2
B. −3/2
C. 0
D. 3

Answer: B) −3/2

Explanation: |a + b + c|² = 0. Expanding: |a|² + |b|² + |c|² + 2(a.b + b.c + c.a) = 0. Since they are unit vectors, 1 + 1 + 1 + 2(a.b + b.c + c.a) = 0, leading to a.b + b.c + c.a = −3/2.

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