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in Vector algebra by (36.3k points)

Let a, b and c be unit vectors such that a + b + c = 0, Which one of the following is correct? 

(a) a × b = b × c = c × a = 0 

(b) a × b = b × c = c × a ≠ 0 

(c) a × b = b × c = a × c ≠ 0 

(d) a × b, b × c, c × a are mutually perpendicular

1 Answer

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Best answer

Answer is (b) a × b = b × c = c × a ≠ 0

Explanation:

Given a + b + c = 0 

a + b = – c 

a × (a + b) = –a × c 

(a × b) = c × a ...(i)

Also, a + c = – b

b × (a + c) = – b × b 

b × c = – b × a = a × b ...(ii)

From (i) and (ii), we get,

a × b = b × c = c × a 

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