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find all the possible triplets (a(1), a(...

find all the possible triplets `(a_(1), a_(2), a_(3))` such that `a_(1)+a_(2) cos (2x)+a_(3) sin^(2) (x)=0` for all real x.

A

vectors `a=a_(1)hati + a_(2)hatj + a_(3)hatk` and `b=4hati + 2hatj + hatk` are perpendicular to each other

B

vectors `a=a_(1)hati + a_(2)hatj + a_(3)hatk` and `b=-hati+hatj + 2hatk` are perpendicular to each other

C

If vector `a=a_(1)hati + a_(2)hatj + a_(3)hatk`of length `sqrt(6)` units , then one of the ordered triplet `(a_(1),a_(2),a_(3)) =(1,-1,-2)`

D

If vectors `2a_(1) + 3a_(2) + 6a_(3)`,then `|a_(1)hati + a_(2)hatj + a_(3)hatk|` is `2sqrt(6)`

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