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Consider three vectors vec A=hat i+hat j...

Consider three vectors `vec A=hat i+hat j-2hat k, vec B=hat i-hat j+hat k` and `vec C=2hat i-3hat j+4hat k`. A vector `vec X` of the form `alphavec A+betavec B` ( `alpha` and `beta` are numbers ) is perpendicular to `vec C` .The ratio of `alpha` and `beta` is

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