InterviewSolution
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InterviewSolution
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Let ` vecu = u_(1)hati + u_(2)hatj +u_(3)hatk` be a unit vector in ` R^(3) and vecw = 1/sqrt6 ( hati + hatj + 2hatk)` , Given that there exists a vector `vecv " in " R^(3)` such that ` | vecu xx vecv| =1 and vecw . ( vecu xx vecv) =1` which of the following statements is correct ?A. There is exactly one choice for such ` vecv`B. There are exactly two for such `vecv`C. There are exactly for such `vecv`D. There are infinitely many choices for such `vecv` |
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Answer» Correct Answer - D Clearly, `vecw` is a unit vector such that ` |vecu xx vecv|=1 and vecw , (vecu xx vecv) =1 ` Now, ` ` vecw .(vecu xx vecv) =1` ` Rightarrow vecw = vecu xx vecv` ` Rightarrow |vecw| = |vecu xx vecv|` ` Rightarrow 1 = |vecu||vecv| sin theta " where " theta` is the angle betweeen ` vecu and vecv` ` Rightarrow vecc sin theta =1` Clearly, p can take infinitely many positions on the line at a unit distance from OA. Consequently, ` vec(OP) =vecv` has, infinitely, many chocies. |
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