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
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
