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if i, j, k be unit orthonormal vectors and a be any, also a×r=j then a.r is equal to (1)0 (2)1 (3)-1 (4) Arbitrary scalar
We have |a x r|² + |a.r|² = |a|² |r|²| j|² + (a. r)² = |a|² |r|²(a. r) = + - (|a|² |r|² - 1) This shows that (a. r) depends on |r | on a given a. Hence (a.r) is any arbitrary scalar.Option D is correct. RegardsArun(askIITians forum expert)
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