Statement 1: The vectors a, b and c lie in the same plane if and only if a ( b c) = 0 Statement 2: The vectors u and v are perpendicular if and only if u v = 0 where u v is a vector perpendicular to the plane of u and v

JEE Main 2012 Mathematics question

Statement 1: The vectors , and lie in the same plane if and only if Statement 2: The vectors and are perpendicular if and only if where is a vector perpendicular to the plane of and

(1)Statement 1 is false, Statement 2 is true.
(2)Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement 1.
(3)Statement 1 is true, Statement 2 is false.
(4)Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.Correct

Answer: (4)

Solution

Three vectors are coplanar iff their scalar triple product vanishes — Statement 1 true. Non-zero vectors are perpendicular iff their dot product is zero, and is indeed

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Question ID VK-103710