InterviewSolution
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InterviewSolution
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Let ` overset(to)(a) =a_(1) hat(i) + a_(2) hat(j) + a_(3) hat(k) , overset(to)(a) = b_(1) hat(i) +b_(2) hat(j) +b_(3) hat(k) " and " overset(to)(a) = c_(1) hat(i) +c_(2) hat(j) + c_(3) hat(k)` be three non- zero vectors such that `overset(to)(c )` is a unit vectors perpendicular to both the vectors `overset(to)(c )` and `overset(to)(b)`. If the angle between `overset(to)(a) " and " overset(to)(n)` is `(pi)/(6)` then `|{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}|` is equal to |
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Answer» Correct Answer - c We are given that `veca = a_(1)hati+a_(2)hatj +a_(3)hatk` `vecb = b_(1)hati +b_(2)hatj +b_(3)hatk` `vecc =c_(1)hati +c_(2)hatj +c_(3)hatk` `"then"|{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|^(2)=[veca vecbvecc]^(2)` ` (veca xx vecb.vecc)^(2)` `(|veca xx vecb|.1cos)^(@2)` (since `vecc` is `bot "to" veca and vecb, vecc "is " bot "to" vecaxx vecb)` `(|veca xx vecb|)^(2)` `(|veca||vecb|.sin""pi/6)^(2)` `(1/2sqrt(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))sqrt(b_(1)^(2)+b_(2)^(2)+b_(3)^(2)))^(2)` `1/4(a_(1)^(2)+a_(2)^(2)+a_(2)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))` |
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