Let u =u_1 i +u_2 j +u_3 k be a unit vector in R ^3 and w = 1 6 ( i + j +2 k ). Given that there exists a vector v in R ^3 such that | u v |=1 and w ( u v )=1. Which of the following statement(s) is(are) correct?

JEE Advanced 2016 Mathematics question

Let be a unit vector in and . Given that there exists a vector in such that and . Which of the following statement(s) is(are) correct?

Answer: (B),(C)

is a vector of magnitude 1 whose dot product with the unit vector is 1, so . This requires : . If is one solution, then is also a

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Question ID VK-026587