Let a → = i ^ + j ^ - k ^ and b → = 2 i ^ - j ^ + k ^ . If c → is a non-zero vector perpendicular to both a → and b → , such that its component along x , y , z axes are rational numbers, then c → is

Question

Let a → = i ^ + j ^ - k ^ and b → = 2 i ^ - j ^ + k ^ . If c → is a non-zero vector perpendicular to both a → and b → , such that its component along x , y , z axes are rational numbers, then c → is, an integer, an irrational number, a rational number, None of these

MARKS App · Accepted Answer

c → = λ a → × b → = λ i ^ j ^ k ^ 1 1 − 1 2 − 1 1 = − 3 λ j ^ + k ^ c → = 3 2 λ Hence, an irrational number

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